m 4. , using the following steps. In(x) xxx0.01 Compute lim In(x) xxx100 We want to obtain the limit lim Compute lim In x xxxm " > In(x) In(. Do you think the result would change for lim lim x→∞ X xx x0.00 What do your answers to (a) through (c) hint about the relativ dxm, m > 0, as x grows very large? Explain in words, and de > 0.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 4.
number, using the following steps.
In(x)
xxx0.01.
In(x)
xxx100
(a) Compute lim
In x
We want to obtain the limit lim
"
xx xm
(b) Compute lim
(c) Do you think the result would change for lim
where m is a positive
9
In(x)
In(x)
lim
X→∞ X xxx0.00001
xxx100000
(d) What do your answers to (a) through (c) hint about the relative rates of growth of In(x)
In x
In(x)
or lim
-?
and xm, m > 0, as a grows very large? Explain in words, and deduce the value lim for
m > 0.
xx xm
Transcribed Image Text:Problem 4. number, using the following steps. In(x) xxx0.01. In(x) xxx100 (a) Compute lim In x We want to obtain the limit lim " xx xm (b) Compute lim (c) Do you think the result would change for lim where m is a positive 9 In(x) In(x) lim X→∞ X xxx0.00001 xxx100000 (d) What do your answers to (a) through (c) hint about the relative rates of growth of In(x) In x In(x) or lim -? and xm, m > 0, as a grows very large? Explain in words, and deduce the value lim for m > 0. xx xm
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