(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use the Le'Hopitals rule to prove the following. Let F be differentiable on (0, infinity) and a> 0. If

[tex] \lim_{x-> \infty} (af(x)+2x^{1/2}f'(x)) =L [/tex] then [tex] lim_{x-> \infty}f(x)= \frac{L}{a} [/tex]

3. The attempt at a solution

It seems to me that what I need to prove is that

[tex] lim _{x-> \infty} 2x^{1/2}f'(x)) =0 [/tex] I'm pretty lost as to how to go about it,

I've tried to define a function [tex] g(x) = \frac{f(x)}{sqrt(x)} [/tex] but that didn't help.

My problem are that:

1. I don't know if f' is differentiable or not.

2. if f converges to L/a then it doesnt satisfy the requirments of the Le'Hopital rule.

3. I'm inclined to say that if a function converges then it's derivative converges to 0. This seems intuitive but I'm not sure how to prove it.

Thanks for the help

Tal

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Le'Hopital Rule

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