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Hello everyone, I am just new to this forum and also a beginner at calculus.

I have a question from my textbook. It's:

Find an example of f(x) that satisfies the following conditions :

f(x) is differentiable for all x>0;

lim_{x->∞}f(x) =2;

lim_{x->∞}f'(x) does not exist;

I think that if f(x) satisfies the second condition it must have a horizontal tangent at infinity,which means f'(x) = 0 at infinity, am I right? and what does "f'(x) does not exist" really mean?

Thanks in advance.

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: Question on limit at infinity

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