HP 40gs - Manual (Page 300)

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