HP 40gs - 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
---
xd
0
2
∫
=
gx()
2x 3+
x 2+
---------------
=
3
2
---
gx()
7
4
---
≤≤
3
2
---
e
x
n
---
gx()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 12:27 AM