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can someone help me to see whether the following statements choose or false

a) if lim(X->infinite)f(x) exists and is finite and lim(X->infinite)f'(x)=b then b=0

i think it is right but i don't know how to prove it

b)if lim(X->infinite)f(x) exists and is finite then lim(X->infinite)f'(x)=0

i have no idea guesses right

c)lim(X->infinite)f'(x)=0 then lim(X->infinite)f(x) exists

counterexample: f(x)=lnx

d))lim(X->infinite)f'(x)=0 then lim(X->infinite)f(x)/x=0

no idea as well

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# Homework Help: Differentiable statements

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