HP 40gs User Manual page 296

hp40g+.book Page 22 Friday, December 9, 2005 1:03 AM
Exercise 8
Part 1
16-22
For this exercise, make sure that the calculator is in exact
real mode with X as the current variable.
For an integer, n, define the following:
x
-- -
2
2x + 3
n
∫
-------------- - e
u = x d
n
x + 2
0
Define g over [0,2] where:
2x + 3
g x ( )
-------------- -
=
x + 2
1. Find the variations of g over [0,2]. Show that for
every real x in [0,2]:
3 7
≤ g x ( ) ≤
-- - -- -
2 4
2. Show that for every real x in [0,2]:
x x x
-- - -- - -- -
3 7
n n n
≤ g x ( )e ≤
-- - e -- - e
2 4
3. After integration, show that:
2
-- -
⎛ ⎞ ⎛
3 7
n
≤ ≤
-- - ne -- - ne
⎜ – n ⎟ u ⎜
n
2 4
⎝ ⎠ ⎝
4. Using:
x
e – 1
lim ------------- = 1
x
→
x 0
u
show that if has a limit L as n approaches infinity,
n
then:
7
≤ ≤
-- -
3 L
2
2
-- -
⎞
n
– n ⎟
⎠
Step-by-Step Examples