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Homework Statement
Given f is differentiable on (0,\infty)
Given lim_{x->\infty} [f(x)+f'(x)]=L
S.T lim f(x)=L and lim f'(x)=0
Hint f(x)=e^{x}f(x)/e^{x}
Homework Equations
The Attempt at a Solution
A Lim _{x->\infty} [f(x)+f'(x)]=L
Then for some \epsilon>0
|f(x)+f'(x)-L|<\epsilon
Tried different approaches by substituting for f(x) and f'(x) based on the hint. But did not help. I tried to get it to a L/infinity form so f'(x)=0 but could not.