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## Homework Statement

Given f is differentiable on (0,[tex]\infty[/tex])

Given [tex]lim_{x->[tex]\infty[/tex]}[/tex] [f(x)+f'(x)]=L

S.T lim f(x)=L and lim f'(x)=0

Hint f(x)=e[tex]^{x}[/tex]f(x)/e[tex]^{x}[/tex]

## Homework Equations

## The Attempt at a Solution

A Lim [tex]_{x->[tex]\infty[/tex]}[/tex] [f(x)+f'(x)]=L

Then for some [tex]\epsilon[/tex]>0

|f(x)+f'(x)-L|<[tex]\epsilon[/tex]

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.