HP 40gs User Manual page 300

hp40g+.book Page 26 Friday, December 9, 2005 1:03 AM
Part 2
16-26
:
The variable VX is now set to N. Reset it to X by
NOTE
pressing (to display CAS MODES screen)
and change the INDEP VAR setting.
To check the result, we can say that:
x
e – 1
lim ------------- = 1
x
→
x 0
and that therefore:
2
-- -
n
e – 1
lim ------------- - = 1
2
→ + ∞
n
-- -
n
or, simplifying:
2
-- -
⎛ ⎞
n
n ⋅
⎜ ⎟
lim e – 1 = 2
⎝ ⎠
→ + ∞
n
L u
If the limit of exists as
n
inequalities in solution 2 above, we get:
3 7
-- - 2 ⋅ L ≤ ≤ -- - 2 ⋅
2 4
1. Show that for every x in [0,2]:
2x + 3 1
-------------- - ----------- -
= 2 –
x + 2 x + 2
2. Find the value of:
2
2x + 3
∫
-------------- - dx
I =
x + 2
0
3. Show that for every x in [0,2]:
x 2
-- - -- -
n n
≤ ≤
1 e e
4. Deduce that:
2
-- -
n
≤ ≤ I ⋅
1 u e
n
u
5. Show that is convergent and find its limit, L.
n
∞
n approaches +
in the
Step-by-Step Examples