HP 40gs - Manual (Page 296)

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