3. let f: R>IR be adipperenthablequnchon such।॥ १९that FCO) =dand Fle> if z70131the interuala) By using an apiopisk[gx] prove that fax) 7DC if x70thesem onbi Prodeb, Prave that lim fue) = 0

Answered: 3. Let fi R>R be a dipperentiabe…

3. Let fi R>R be a dipperentiabe quachon such and Fleo>7 if 2J0 the interual FCO) =d a) By using an appropiake therem on [gx] prove that Fax) 77 If X70 L Prose 62 Prove that lim fex) =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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Question

3. let f: R>IR be a
dipperenthablequnchon such
।॥ १९
that FCO) =d
and Fle> if z70
131
the interual
a) By using an apiopisk
[gx] prove that fax) 7DC if x70
thesem on
bi Prode
b, Prave that lim fue) = 0

Expert Solution

Step 1

Given that: F(x) is a differentiable function and it satisfies the following properties.

$F' (x) >7$ if x > 0
$F (0) =0$

To show:

$On interval [0, x], F (x) > 7 x if x>0$
$\lim_{x \to \infty} F (x) = \infty$

Step by step

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