HP 40gs User Manual page 302

16-28
Solution 3
The calculator is not needed here. Simply stating that
x
-- -
n
e x
increases for
inequality:
x 2
-- - -- -
n n
≤ ≤
1 e e
Solution 4
g x ( )
is positive over [0, 2], through multiplication
Since
we get:
x
-- -
n
g x ( ) g x ( )e ≤
and then, integrating:
2
-- -
n
≤ ≤
I u e I
n
Solution 5
First find the limit of
→ + . ∞
n
when
Note: pressing
after you have selected the
infinity sign from the
character map places a "+"
character in front of the infinity sign.
Selecting the entire
expression and pressing
yields:
1
2
-- -
In effect, tends to 0 as
n
∞
tends to + , so
e
∞ u
n tends to + ,
As
quantity that tends to .
u
Hence, converges, and its limit is .
n
We have therefore shown that:
∈
[ , ] 0 2
is sufficient to yield the
2
-- -
n
≤ g x ( )e
2
-- -
n
e
n
2
-- -
0
e = 1
n tends to
is the portion between
n
I
L =
∞
n tends to + .
as
I
and a
I
I = 4 – ln 2
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