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16-28 Step-by-Step Examples
Solution 3
The calculator is not needed here. Simply stating that
increases for is sufficient to yield the
inequality:
Solution 4
Since is positive over [0, 2], through multiplication
we get:
and then, integrating:
Solution 5
First find the limit of
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
In effect, tends to 0 as
tends to + , so tends to as tends to + .
As tends to + , is the portion between and a
quantity that tends to .
Hence, converges, and its limit is .
We have therefore shown that:
e
x
n
---
x 02[,]∈
1 e
x
n
---
e
2
n
---
≤≤
gx()
gx() gx()e
x
n
---
gx()e
2
n
---
≤≤
Iu
n
e
2
n
---
I≤≤
e
2
n
---
n ∞
2
n
---
n
∞
e
2
n
---
e
0
1= n ∞
n ∞ u
n
I
I
u
n
I
LI42ln–==
hp40g+.book Page 28 Friday, December 9, 2005 1:03 AM