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Texas Instruments TI-84 Plus Manual

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TI-83, TI-83 Plus, TI-84 Plus Guide
Guide for Texas Instruments TI-83,
TI-83 Plus, or TI-84 Plus Graphing
Calculator
This Guide is designed to offer step-by-step instruction for using your TI-83, TI-83 Plus, or TI-84
Plus graphing calculator with the fourth edition of Calculus Concepts: An Informal Approach to
the Mathematics of Change. You should utilize the subject index on page 114 for this Guide to
find the location of a specific topic on which you need instruction.

Setup Instructions

Before you begin, check the calculator setup to be certain that the settings described
below are chosen. Whenever you use this Guide, we assume (unless instructed otherwise)
that your calculator settings are as shown in Figures 1, 2, and 3.
• Press
and choose the settings shown in Figure 1 for the basic setup.
MODE
• Specify the statistical setup with
, 2ND 3 , 2ND 4 , 2ND 5 ,
Figure 2.
• Check the window format by pressing
settings shown in Figure 3.
If you do not have the darkened choices shown in Figure 1 and Figure 3, use the
arrow keys to move the blinking cursor over the setting you want to choose and
press
ENTER
Press
2ND
MODE (QUIT)
TI-84 Plus Basic Setup
Figure 1
Copyright © Houghton Mifflin Company. All rights reserved.
STAT 5 [SetUpEditor]
and
2ND
.
to return to the home screen.
TI-84 Plus Statistical
Setup
Figure 2
followed by
. Press
2ND 6
ENTER
ZOOM (FORMAT)
TI-84 Plus Window Setup
2ND 1 ,
2ND 2
to view the screen in
and choose the
Figure 3
1

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Summary of Contents for Texas Instruments TI-84 Plus

  • Page 1 TI-83, TI-83 Plus, TI-84 Plus Guide Guide for Texas Instruments TI-83, TI-83 Plus, or TI-84 Plus Graphing Calculator This Guide is designed to offer step-by-step instruction for using your TI-83, TI-83 Plus, or TI-84 Plus graphing calculator with the fourth edition of Calculus Concepts: An Informal Approach to the Mathematics of Change.

  • Page 2: Basic Operation

    TI-83, TI-83 Plus, TI-84 Plus Guide Basic Operation You should be familiar with the basic operation of your calculator. With your calculator in hand, go through each of the following. 1. CALCULATING You can type in lengthy expressions; just be certain that you use parentheses to control the calculator's order of operations.
  • Page 3 TI-83, TI-83 Plus, TI-84 Plus Guide The “to a fraction” key is obtained by pressing MATH 1 [ Frac]. The calculator’s symbol for times 10 . Thus, 7.945 means 7.945*10 or 7,945,000,000,000. − 6 − 6 The result means 1.4675 * 10 , which is the scientific 1.4675...
  • Page 4 TI-83, TI-83 Plus, TI-84 Plus Guide If you try to store something to a particular memory location that is being used for a different type of object, a DATA error results. Consult either Troubleshooting the TYPE Calculator in this Guide or your particular calulator Owner’s Guidebook.
  • Page 5 TI-83, TI-83 Plus, TI-84 Plus Guide Chapter 1 Ingredients of Change: Functions and Linear Models 1.1 Models and Functions Graphing a function in an appropriate viewing window is one of the many uses for a function that is entered in the calculator’s graphing list. Because you must enter a function formula on one line, it is important to use parentheses whenever they are needed.
  • Page 6 Chapter 1 Press to set the view for the graph. Enter 0 for WINDOW Xmin and 20 for (For 10 tick marks between 0 and 20, enter 2 Xmax. If you want 20 tick marks, enter 1 for etc. Xscl. Xscl, Xscl does not affect the shape of the graph.
  • Page 7 TI-83, TI-83 Plus, TI-84 Plus Guide Press and the input value is substituted in the function. ENTER The input and output values are shown at the bottom of the screen. (This method works even if you do not see any of the graph on the screen.)
  • Page 8 Chapter 1 EVALUATING OUTPUTS ON THE HOME SCREEN The input values used in the eval- uation process are actual values, not estimated values such as those generally obtained by tracing near a certain value. We again consider the function v(t) = 3.5(1.095 Using x as the input variable, enter .
  • Page 9 TI-83, TI-83 Plus, TI-84 Plus Guide Press , and observe the list of input GRAPH (TABLE) and output values. Notice that you can scroll through the table with , and/or The table values may be ▼ , ▲ ◄ ► .
  • Page 10 Chapter 1 If you already have in the graphing list, you Y1 = 3.622(1.093^X) can refer to the function as in the If not, you can SOLVER. enter instead of in the location of the 3.622(1.093^X) eqn: Press SOLVER. ENTER . If you need to edit the equation, press until the previous ▲...
  • Page 11 TI-83, TI-83 Plus, TI-84 Plus Guide 1. Enter the function in some location of the graphing list – say and draw a graph of the function. Press Y1 = 3.5(1.095^X) and hold down either until you have an TRACE ►...
  • Page 12 Chapter 1 Press and clear all locations with Enter the func- CLEAR . tion 3x – 0.8x + 4 – 2.3 in . You can enter x with X,T,θ,n or enter it with . Remember to use , not X,T,θ,n ^ 2 −...
  • Page 13 TI-83, TI-83 Plus, TI-84 Plus Guide Draw the graphs with ZOOM 4 [ZDecimal] ZOOM 6 If you use the former, press and reset [ZStandard]. WINDOW to get a better view the graph. (If you Xmax Ymax reset the window, press to draw the graph.)
  • Page 14 Chapter 1 Enter to obtain the sum function (f + g)(x) = f(x) + g(x). Y1 + Y2 Enter to obtain the difference function (f – g)(x) = f(x) – g(x). Y1 – Y2 ⋅ ⋅ Enter to obtain the product function (f g)(x) = f(x) Y1*Y2 g(x).
  • Page 15 TI-83, TI-83 Plus, TI-84 Plus Guide Press and clear each previously entered equation with Y= , Enter M in by pressing CLEAR . . 02 X,T,θ,n + 1 . and input S in by pressing 90 ENTER . 5 ( ^ X,T,θ,n ) ENTER .
  • Page 16 Chapter 1 To locate where , press Y1 = Y2 2ND TRACE (CALC) 5 Press to mark the first curve. The cursor [intersect]. ENTER jumps to the other function – here, the line. Next, press to mark the second curve. Next, supply a guess for ENTER the point of intersection.
  • Page 17 TI-83, TI-83 Plus, TI-84 Plus Guide Press and, using one of the arrow keys, move the cursor until it covers the darkened = in . Press . Then, ENTER press until the cursor covers the darkened = in . Press ▼...
  • Page 18 Chapter 1 In this text, we usually use list for the input data and list for the output data. If there are any data values already in your lists, first delete any “old” data using the following procedure. (If your lists are clear, skip these instructions.) DELETING OLD DATA Whenever you enter new data in your calculator, you should first delete any previously entered data.
  • Page 19 TI-83, TI-83 Plus, TI-84 Plus Guide Have the data given in Table 1.1 in Section 1.2 of Calculus Concepts entered in your calculator. Exit the list menu with MODE (QUIT). To run the program, press followed by the number that...
  • Page 20 Chapter 1 • Lists can be named and stored in the calculator’s memory for later recall and use. Refer to p.23 of this Guide for instructions on storing data lists and later recalling them for use. CAUTION: Any time that you enter the name of a numbered list (for instance: , and so forth), you should use the calculator symbol for the name, not a name that you type with the alphabetic and numeric keys.
  • Page 21 TI-83, TI-83 Plus, TI-84 Plus Guide data were constant at $541, so a linear function fit the data perfectly. What information is given by the first differences for these modified tax data? Run program by pressing followed by the DIFF...
  • Page 22 Chapter 1 find a linear function for input data in list and output data in list and paste the equation into graphing location STAT ► [CALC] 4 [LinReg(ax+b)] 3 (L3) , 2nd 4 (L4) , VARS ► [Y−VARS] 1 [Function] 2 [Y2] ENTER . CAUTION: The r that is shown is called the correlation coefficient.
  • Page 23 TI-83, TI-83 Plus, TI-84 Plus Guide Press to access the data lists. To copy the con- STAT 1 [EDIT] tents of one list to another list; for example, to copy the contents , use to move the cursor so that ▲...
  • Page 24 Chapter 1 • There are many ways that you can enter the aligned input into . One method that you may prefer is to start over from the beginning. Replace with the contents of highlighting and pressing Once again highlight the name 2ND 3 (L3) ENTER .
  • Page 25 TI-83, TI-83 Plus, TI-84 Plus Guide Press to return to the home screen. You MODE (QUIT) can view any list from the mode (where the data is STAT EDIT originally entered) or from the home screen by typing the name...
  • Page 26 Chapter 1 Press To delete another list, use to move ENTER . ▼ ▲ the cursor opposite that list name and press Exit this ENTER . screen with when finished. MODE (QUIT) WARNING: Be careful when in the menu. Once you delete something, it is gone DELETE from the calculator’s memory and cannot be recovered.
  • Page 27 TI-83, TI-83 Plus, TI-84 Plus Guide Use the tick marks to estimate rise divided by run and note a possible y-intercept. After pressing to resume the ENTER program, enter your guess for the slope and y-intercept. After entering your guess for the y-intercept, your line is drawn and the errors are shown as vertical line segments on the graph.
  • Page 28 Chapter 1 HAVING THE CALCULATOR ENTER EVENLY SPACED INPUT VALUES When an input list consists of many values that are the same distance apart, there is a calculator command that will generate the list so that you do not have to type the values in one by one. The syntax for this sequence command is seq(formula, variable, first value, last value, increment).
  • Page 29 TI-83, TI-83 Plus, TI-84 Plus Guide We continue to use the data in Table 1.17 of the text. Our input data is already small so we need not align to smaller values. Return to the home screen. Following the same procedure that...
  • Page 30 Chapter 1 Delete (with ) any functions CLEAR that are in the list. A scatter plot of the data drawn with ZOOM 9 shows the slow decline that [ZoomStat] can indicate a log model. As when modeling linear and exponential functions, find and paste the log equation into the location of the list by...
  • Page 31 TI-83, TI-83 Plus, TI-84 Plus Guide using followed by the number of the desired function loca- VARS ► [Y−VARS] 1 [Function] tion. The calculator does not recognize as the name of a function in the list. ALPHA 1 (Y) 1.4 Logistic Functions and Models This section introduces the logistic function that can be used to describe growth that begins as exponential and then slows down to approach a limiting value.
  • Page 32 Chapter 1 TI-84 Plus.) As you did when finding an exponential equation for data, large input values must be aligned or an error or possibly an incorrect answer could be the result. Note that the calculator finds a “best-fit” logistic function rather than a logistic function with a limiting value L such that no data value is ever greater than L.
  • Page 33 TI-83, TI-83 Plus, TI-84 Plus Guide RECALLING MODEL PARAMETERS Rounding function parameters can often lead to incorrect or misleading results. You may find that you need to use the complete values of the coefficients after you have found a function that best fits a set of data. It would be tedious to copy all these digits in a long decimal number into another location of your calculator.
  • Page 34 Chapter 1 Return to the home screen. Now we find the exponential function and paste the equation into the location of the list by pressing STAT ► [CALC] 0 [ExpReg] VARS ► [Y−VARS] 1 [Function] 1 [Y1]. Press to find the equation and paste it into the ENTER location.
  • Page 35 TI-83, TI-83 Plus, TI-84 Plus Guide This situation calls for shifting the data vertically so that it ap- proaches a lower asymptote of y = 0,which is what the logistic function in the calculator has as its lower asymptote for an increasing logistic curve.
  • Page 36 Chapter 1 Press Choose in the WINDOW (TBLSET). Indpnt: location by placing the cursor over and pressing ENTER . (Remember that the other settings on this screen do not matter if you are using Press Delete any values that appear GRAPH (TABLE).
  • Page 37 TI-83, TI-83 Plus, TI-84 Plus Guide Have u(x) = in the location of the list. (Be certain that you remember to enclose both the numerator and denominator of the fraction in parentheses.) A graph drawn with is a starting point.
  • Page 38 Chapter 1 Delete the values currently in the table To numerically estimate u(x), enter values to the right of, and closer and closer − x→ − 2/9. Because the output values appear to become larger and u(x) → − ∞. larger, we estimate that −...
  • Page 39 TI-83, TI-83 Plus, TI-84 Plus Guide Draw a graph of h with Press ZOOM 4 [ZDecimal]. ZOOM 2 and use to move the blinking cursor [Zoom In] ◄ ▲ − until you are near the point on the graph where x = 1.
  • Page 40 Chapter 1 Run program and observe the first differences in list DIFF the second differences in , and the percentage differences in list The second differences are close to constant, so a quadratic function may give a good fit for these data. Construct a scatter plot of the data.
  • Page 41 TI-83, TI-83 Plus, TI-84 Plus Guide First, clear your lists, and then enter the data. Next, align the input data so that x represents the number of years since 1980. (We do not have to align here, but we do so in order to have smaller coefficients in the cubic function.)
  • Page 42 Chapter 1 Press to find the input at the point of intersection. ENTER Because x is the number of years after 1980, the answer to the question posed in part c of Example 3 is either 1984 or 1985. The price had not exceeded $6 in 1984, so the answer to the question is 1985.
  • Page 43 TI-83, TI-83 Plus, TI-84 Plus Guide Chapter 2 Describing Change: Rates As you calculate average and other rates of change, remember that every numerical answer in a context should be accompanied by units telling how the quantity is measured. You should also be able to interpret each numerical answer.
  • Page 44 Chapter 2 next is type and press . Then, store the next set of inputs into A and/or B and ENTER recall using to recall each instruction. Press and you ENTER (ENTRY) ENTER have the average rate of change between the two new points. Try it. FINDING PERCENTAGE CHANGE You can find percentage changes using data either by the formula or by using program...
  • Page 45 TI-83, TI-83 Plus, TI-84 Plus Guide Press . An APR of approximately 11.57% ALPHA ENTER compounded monthly will yield $1,000,000 in 40 years on an initial investment of $10,000. We continue with part b of Example 4 of Section 2.1 of Calculus Concepts to illustrate finding the APY that corresponds to an APR of approximately 0.11568.
  • Page 46 Chapter 2 Use the arrow keys to move the cursor to the opposite corner of your “zoom” box. Point A should be close to the center of your box. Press to magnify the portion of the graph that is inside ENTER the box.
  • Page 47 TI-83, TI-83 Plus, TI-84 Plus Guide VISUALIZING THE LIMITING PROCESS This section of the Guide is optional, but it might help you understand what it means for the tangent line to be the limiting position of secant lines. Program is used to view secant lines between a point (a, f(a)) and close SECTAN points on a curve y = f(x).
  • Page 48 Chapter 2 In this section, we investigate what the calculator does if you ask it to draw a tangent line where the line cannot be drawn. Consider these special cases: 1. What happens if the tangent line is vertical? We consider the function f(x) = (x + 1) which has a vertical tangent at x = –...
  • Page 49 TI-83, TI-83 Plus, TI-84 Plus Guide 3a. Clear and enter, as indicated, the function R S | ≤ when . (The inequality symbols are > when accessed with MATH (TEST). Set each part of the function to draw in mode by placing the cursor over the equals...
  • Page 50 Chapter 2 2.3 Derivative Notation and Numerical Estimates CALCULATING PERCENTAGE RATE OF CHANGE Percentage rate of change = rate of change at a point ⋅ . We illustrate calculating the percentage rate of change 100% value of the function at that point with the example found on page 134 in Section 2.3 of Calculus Concepts.
  • Page 51 TI-83, TI-83 Plus, TI-84 Plus Guide Continue in this manner, recording each result on paper, until you can determine to which value the slopes from the left seem to be getting closer and closer. It appears that the slopes of the secant lines from the left are approaching 5.706 billion dollars per year.
  • Page 52 Chapter 2 many decimal places as are necessary to determine the limit to the desired degree of accuracy. • Note: You may wish to leave the slope formula in as long as you need it. Turn when you are not using it. 2.4 Algebraically Finding Slopes The calculator does not find algebraic formulas for slope, but you can use the built-in numerical derivative and draw the graph of a derivative to check any formula that you find...
  • Page 53 TI-83, TI-83 Plus, TI-84 Plus Guide Suppose you want to find the slope of the secant line between the points (0, f(0)) and (2, f(2)). That is, you are finding the − − slope of the secant line between the points (a...
  • Page 54 Chapter 2 These values are those in the fifth row of the above table − the values for k = 0.001. From this point forward, we use k = 0.001 and therefore do not specify k when evaluating Will nDeriv(. the slope of this secant line always do a good job of approximating the slope of the tangent line when k = 0.001? Yes, it generally does, as long as the instantaneous rate of change exists at the input value at which you evaluate...
  • Page 55 TI-83, TI-83 Plus, TI-84 Plus Guide Chapter 3 Determining Change: Derivatives 3.3 Exponential and Logarithmic Rate-of-Change Formulas The calculator only approximates numerical values of slopes – it does not give a slope in formula form. You also need to remember that the CALCULATOR calculates the slope (i.e., the derivative) at a specific input value by a different method than the one we use to calculate the slope.
  • Page 56 Chapter 3 Press and edit to be the function g ( x ) = 2 Access the statistical lists, clear any previous entries from , and . Enter the x -values shown above in . Highlight and enter . Remember to type using Y1(L1) 2ND 1 (L1).
  • Page 57 TI-83, TI-83 Plus, TI-84 Plus Guide The slope appears at the bottom of the screen. dy/dx = 2.0666667 Return to the home screen and press The calculator’s X,T,θ,n . memory location has been updated to 3. Now type the numerical derivative instruction (evaluated at 3) as shown to the right.

  • Page 58: The Chain Rule

    Chapter 3 Start with Neither ZOOM 4 [ZDecimal] or ZOOM 6 [ZStandard]. of these shows a graph (because of the large coefficient in the function), but you can press to see some of the output TRACE values. Using those values, reset the window. The graph to the −...
  • Page 59 TI-83, TI-83 Plus, TI-84 Plus Guide Chapter 4 Analyzing Change: Applications of Derivatives 4.2 Relative and Absolute Extreme Points Your calculator can be very helpful for checking your analytic work when you find optimal points and points of inflection. When you are not required to show work using derivative formulas or when an approximation to the exact answer is all that is required, it is a simple process to use your calculator to find optimal points and inflection points.
  • Page 60 Chapter 4 Press to mark the location of the right bound. You are ENTER next asked to provide a guess. Any value near the intercept will do. Use to move the cursor near the intercept. ◄ Press The location of the x-intercept is displayed. ENTER .
  • Page 61 TI-83, TI-83 Plus, TI-84 Plus Guide Reset to a larger value, say 95,000, to better see the high Ymax point on the graph. Graph R and press Hold down TRACE . until you have an estimate of the input location of the high ►...
  • Page 62 Chapter 4 Press to mark the left bound of the interval. Use ENTER to move the cursor to the right of the high point on the ► curve. Press to mark the right bound of the interval. Use ENTER to move the cursor to your guess for the high point on the ◄...
  • Page 63 TI-83, TI-83 Plus, TI-84 Plus Guide Enter f in the location of the list, the first derivative of f , and the second derivative of f in . (Be careful not to round any decimal values.) Turn off We are given the input interval 1982 through 1990, so 0 ≤ x ≤ 8.
  • Page 64 Chapter 4 Find the x-intercept of the second derivative graph as indicated in this section or find the input of the high point on the first derivative graph (see page 63 of this Guide) to locate the inflection point. 5.3.2 USING THE CALCULATOR TO FIND INFLECTION POINTS Remember that an inflection point on the graph of a function is a point of greatest or least slope.
  • Page 65 TI-83, TI-83 Plus, TI-84 Plus Guide If you prefer, you could have found the input of the inflection ′′ point by solving the equation C = 0 using the . (Do SOLVER not forget that drawing the graph of C and tracing it can be used...
  • Page 66 Chapter 5 Chapter 5 Accumulating Change: Limits of Sums and the Definite Integral 5.1 Results of Change and Area Approximations So far, we have used the calculator to investigate rates of change. In this chapter we consider the second main topic in calculus – the accumulation of change. You calculator has many useful features that will assist in your investigations of the results of change.
  • Page 67 TI-83, TI-83 Plus, TI-84 Plus Guide Consider what is now in the lists. contains the left endpoints of the 11 rectangles and contains the heights of the rectangles. If we multiply the heights by the widths of the rectan- gles (1 hour) and enter this product in...
  • Page 68 Chapter 5 With the cursor in , press VARS ► 1 [Function] 1 [Y1] ) ( X,T,θ,n 2ND MATH [TEST] 6 [<] 20 ) VARS ► 1 [Function] 2 [Y2] ) ( X,T,θ,n 2ND MATH [TEST] 3 [>] 20 Your calculator draws graphs by connecting function outputs wherever the function is defined. However, this function breaks at x = 20.
  • Page 69 TI-83, TI-83 Plus, TI-84 Plus Guide AREA APPROXIMATIONS USING RIGHT RECTANGLES We continue with the previous function and find an area approximation using right rectangles. Part a of Example 2 says to find the change in the drug concen- tration from x = 0 through x = 20 using right rectangles of width 2 days.
  • Page 70 Chapter 5 Clear lists . To use 4 midpoint rectangles to approximate the area of the region between the graph of f and the x-axis between x = 0 and x = 2, first enter the midpoints of the rectangles (0.
  • Page 71 TI-83, TI-83 Plus, TI-84 Plus Guide Input at the prompt and press A graph of the 4 ENTER . approximating midpoint rectangles and the function are shown. (Note that the program automatically sets the height of the win- dow based on the left and right endpoints of the input interval.)
  • Page 72 Chapter 5 We illustrate using this program to find a limit of sums using W(x) = − ⋅ − − , the function in Example 4 of Section 5.1 of 1.243 10 0.0314 2.6174 71.977 Calculus Concepts. Begin by entering the function in Y1. Notice that to enter −...
  • Page 73 TI-83, TI-83 Plus, TI-84 Plus Guide Continue in this manner, each time choosing the first option, and doubling until a limit is evident. CHANGE N, Intuitively, finding the limit means that you are sure what the area approximation will be without having to use larger values in the program.

  • Page 74: The Fundamental Theorem Of Calculus

    Chapter 5 • The calculator’s function yields the same result (to 3 decimal places) as that found in fnInt the limit of sums investigation on page 66 of this Guide. 5.3 The Fundamental Theorem of Calculus Intuitively, this theorem tells us that the derivative of an antiderivative of a function is the function itself.
  • Page 75 TI-83, TI-83 Plus, TI-84 Plus Guide Enter f in , and F in , and fnInt(Y1, X, 0, X) , using a different number for C in each function location. (You can use the values of C shown to the right or different values.)
  • Page 76 Chapter 5 Because part a of Example 3 asks for the areas of the regions above and below the input axis and the function, we must find where the function crosses the axis. You can find this value using the solver (solve = 0) or by using the graph and the x-intercept method described on page A-11 of this guide.
  • Page 77 TI-83, TI-83 Plus, TI-84 Plus Guide − and draw the graph of with Xmin = 7, Xmax = 0, ZOOM ▲ [ZoomFit] ENTER . Press The calculator asks TRACE (CALC) 7 [∫f(x)dx]. Press and obtain the screen shown to the Lower Limit? (−)
  • Page 78 Chapter 5 We next find the inputs of the points of intersection of the two functions. (These values will probably be the limits on the integrals we use to find the areas.) The method we use to find the first of the points is the intersection method that was discussed on page A-11 of this Guide. With the graph on the screen, press TRACE (CALC) 5 The calculator asks...
  • Page 79 TI-83, TI-83 Plus, TI-84 Plus Guide − NOTE: The value 18.883666588 – 77.77487813 ≈ 58.8912 could also have been calculated by evaluating fnInt(Y1 − Y2, X, 10, 20) . Because the graph in Figure 5.56 shows that the area fnInt(Y1 − Y2, X, 10, 20)
  • Page 80 Chapter 5 We illustrate for the graph shown above. The area of the rectangle whose height is the average temperature is (94.18647243)(1000) ≈ 94,186.472. Using MATH 9 (fnInt), we find that the area of the region between a t = and t = 0 is ≈...
  • Page 81 TI-83, TI-83 Plus, TI-84 Plus Guide Chapter 6 Analyzing Accumulated Change: Integrals in Action 6.1 Perpetual Accumulation and Improper Integrals NUMERICALLY ESTIMATING END BEHAVIOR Recall from page A-34 of this guide that we can use the calculator to estimate end behavior. We illustrate using the improper ∞...
  • Page 82 Chapter 6 In Example 1, part a , we are told that the business’s profit remains constant. Clear lists . In enter two possi- ble input values for the time involved. (You might use different years than the ones shown here.) In enter the amount invested: 10% of the constant profit.
  • Page 83 TI-83, TI-83 Plus, TI-84 Plus Guide of the data and it should be obvious from the shape of the scatter plot the function to fit to the data. For instance, return to Example 1, part b , in which we are told that the business’s profit grows by $50,000 each year.
  • Page 84 Chapter 6 To determine the 2-year future value, we add the future value of each month’s deposit, beginning with x = 0 (for month 1) and ending with x = 23 (for month 24). The calculator sequence command can be used to find this sum. The syntax for this is seq(formula, variable, first value, last value, increment) Return to the home screen and enter seq(Y1, X, 0, 23, 1).
  • Page 85 TI-83, TI-83 Plus, TI-84 Plus Guide CONSUMER ECONOMICS We illustrate how to find the consumers’ surplus and other economic quantities when the demand function intersects the input axis as given in Example 1 of Section 6.3 of Calculus Concepts: Suppose the demand for a certain model of minivan in the United States can be described as D(p) = 14.12(0.933...
  • Page 86 Chapter 6 The calculator draws the consumers’ surplus if you use the following method. − First, reset to have more room at the bottom of the Ymin graph. Draw the graph of D. Then, with the graph on the screen, press At the TRACE (CALC) 7 [∫f(x)dx].
  • Page 87 TI-83, TI-83 Plus, TI-84 Plus Guide We add the demand function for the gasoline example used on page A-87 of this guide to calculate producers’ willingness and ability to receive. The demand and supply functions for the gasoline example in the text are given by D(p) = 5.43(0.607 million gallons and S(p) = 0 million gallons for p <...
  • Page 88 Chapter 6 Enter in a location of fnInt(Y1, X, E, X) list, say . Turn off . Set the calculator TABLE and enter increasingly larger values of such as those shown to the right. ≈ 4.360, giving social gain 1.108 + 4.360 ≈ $5.5 million. It appears that ≈...
  • Page 89 TI-83, TI-83 Plus, TI-84 Plus Guide To draw a graph of the normal density function, note that nearly all of the area between this function and the horizontal axis lies within three standard deviations of the mean. Set Xmin = 9 – 3 = 6 to draw the graph.
  • Page 90 Chapter 7 Chapter 7 Repetitive Change: Cycles and Trigonometry 7.1 Functions of Angles: Sine and Cosine Before you begin this chapter, go back to the first page of the Graphing Calculator Instruction Guide and check the basic setup, the statistical setup, and the window setup. If these are not set as specified in Figures 1, 2, and 3, you will have trouble using your calculator in this chapter.
  • Page 91 TI-83, TI-83 Plus, TI-84 Plus Guide regression in the calculator, it is sometimes necessary to have an estimate of the period of the data. The data appear to be cyclic. Either view the data or TRACE the scatter plot to measure the horizontal distance between one high point and the next (or between any two successive low points).
  • Page 92 Chapter 7 and not have the correct equation entered. The function (see below) that is entered in incorrect. The correct way to enter the function c is shown in When these two equa- tions are graphed, you can see that they are entirely different functions.
  • Page 93 TI-83, TI-83 Plus, TI-84 Plus Guide Chapter 8 Dynamics of Change: Differential Equations and Proportionality Numerically Estimating by Using Differential Equations: Euler’s Method Many of the differential equations we encounter have solutions that can be found by determin- ing an antiderivative of a given rate-of-change function. Thus, many of the techniques that we learned using the calculator’s numerical integration function apply to this chapter.
  • Page 94 Chapter 8 Run the program. Each time the program stops for input or for you to view a result, press to continue. ENTER We choose to use 16 steps. Enter this value. The interval is 4 length of interval years, so enter the step size = = 0.25.
  • Page 95 TI-83, TI-83 Plus, TI-84 Plus Guide tute a value for k in the differential equation before using program . It is always better EULER to store the exact value for a constant instead of using a rounded value. Enter = 5.9x – 3.2y in .
  • Page 96 ^ ( 4 ALPHA 4 (T) ) . re are many calculator programs, including one that will graph a multivariable function with two input variables, available at the Texas Instruments web site with address http://education.ti.com. Copyright © Houghton Mifflin Company. All rights reserved.
  • Page 97 TI-83, TI-83 Plus, TI-84 Plus Guide Return to the home screen with Access MODE (QUIT). the solver by pressing . If there are no equations MATH 0 stored in the solver, you will see the screen displayed on the right.
  • Page 98 Chapter 9 Step 2: Choose values for v and solve for t to obtain points on the 2000 constant-contour curve. Obtain guesses for the values of v and t from Table 9.2 in the text. Enter the H ( v, t ) formula in .
  • Page 99 TI-83, TI-83 Plus, TI-84 Plus Guide table with the values of the first input variable listed horizontally across the top of the table and the values of the second input variable listed vertically down the left side of the table.
  • Page 100 Chapter 9 NOTE: You may find it helpful to place a piece of paper or a ruler under the row (or to the right of the column) in which the data appear to help avoid entering an incorrect value. You can reuse the input data from Ex. 1 of Section 9.3 and enter the output in L2., Next, clear any functions from the...
  • Page 101 TI-83, TI-83 Plus, TI-84 Plus Guide You can obtain an estimate of the tan- gent line slope with 2ND TRACE (CALC) 6 [dy/dx]. ► ◄ move the cursor as close as possible to = 0.6. Press ENTER . 0.6 is not a trace value.
  • Page 102 Chapter 9 dE e Find evaluated at e = 0.8 to It is not necessary to again store the values for N and be about 0.745 foot per mile. E unless for some reason (Always remember to attach units of they have been changed.
  • Page 103 TI-83, TI-83 Plus, TI-84 Plus Guide NOTE: Remember that 2ND recalls previously-entered statements so ENTER (ENTRY) you do not have to spend time re-entering them. 9.4 Compensating for Change As you have just seen, the TI-83 closely estimates numerical values of partial derivatives using function.
  • Page 104 Chapter 9 FINDING THE SLOPE OF A LINE TANGENT TO A CONTOUR CURVE We con- tinue the previous illustration with the body-mass index function in Example 1 of Section 9.4 of Calculus Concepts. Part a of Example 1 asks for at the point (67, 129) on the contour −...
  • Page 105 TI-83, TI-83 Plus, TI-84 Plus Guide Chapter 10 Analyzing Multivariable Change: Optimization 10.2 Multivariable Optimization As you might expect, multivariable optimization techniques that you use with your calculator are very similar to those that were discussed in Chapter 4. The basic difference is that the algebra required to get the expression that comes from solving a system of equations with several unknowns reduced to one equation in one unknown is sometimes difficult.
  • Page 106 Chapter 10 Now, replace every with the symbol by placing the cursor on each location and pressing VARS ► [Y−VARS] . What you have just done is substitute 1 [Function] 2 [Y2] the expression for from equation 2 in equation 1. The expression in is the left-hand side of an equation that equals 0 and it contains only one variable, namely h.
  • Page 107 TI-83, TI-83 Plus, TI-84 Plus Guide Take the derivative of with respect to h and we have Y2 = , the partial derivative of V with respect to h and then h − again. Find V 72 at the critical point.
  • Page 108 Chapter 10 Consider the cake volume index function in Example 1 of Section 10.2 in Calculus Concepts: − V(l, t) = 3.1l + 22.4l – 0.1t + 5.3t When l grams of leavening is used and the cake is baked at 177 C for t minutes.
  • Page 109 TI-83, TI-83 Plus, TI-84 Plus Guide Return to the home screen. The matrix that holds the solution to the system of equations, provided a solution exists, is − − obtained with (MATRIX) 1 [A] − (MATRIX) 2 [B] ENTER .
  • Page 110 Chapter 10 The numbers at the bot- Using equations [1] and [2] on page tom of the screen give the 109, enter the coefficients of l in the row and column that is first column, the coefficients of t in highlighted.
  • Page 111 TI-83, TI-83 Plus, TI-84 Plus Guide strained optimization problem with the functions given in Example 1 of Section 10.3 – the Cobb-Douglas production function f ( L, K ) = 48.1 L subject to the constraint g ( L, K ) = 8 L + K = 98 where L worker hours (in thousands) and $ K thousand capital investment are for a mattress manufacturing process.
  • Page 112 Chapter 10 Choose a value of that is less than L = 7.35, say 7.3. Find the value of K so that 8 L + K = 98. Remember that , so store K = Y2 7.3 in and call up .
  • Page 113 TI-83, TI-83 Plus, TI-84 Plus Guide 10.3.2 FINDING OPTIMAL POINTS USING MATRICES AND CLASSIFYING OPTIMAL POINTS UNDER CONSTRAINED OPTIMIZATION Remember that a matrix solution method only can be used with a system of linear partial derivative equations. We choose to illustrate the matrix process of solving with matrix Method 2 (discussed on page 110) for the sausage production function in Example 3 of Section 10.3 in Calculus Concepts .
  • Page 114 Chapter 10 g w s = for 0 and Enter P ( w , s ) in Y1. Solve the constraint ( , ) 1 − = + − in Y2. enter ( , ) 1 g w s Access the EQUATION SOLVER with MATH 0 . Enter the eqn: 0 = Y2.

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