Question

Suppose the lim as x->0 of [f(x)]/x equals to 5. What is the lim of f(x) as x->0?

Answer 1

\[\lim_{x \rightarrow 0}\frac{f(x)}{5}=5\] The five is a constant,

\[5*lim_{x \rightarrow 0}\frac{f(x)}{5}=5*5=\frac{5}{5}*lim_{x \rightarrow 0}f(x)\]

Answer 2

\[\lim_{x \rightarrow 0} f(x)/x = 5. What is \lim_{x \rightarrow 0} f(x)?\]

Answer 3

There are two cases where f(x) can exist. f(x) = x * g(x) such that lim_x->0 f(x) = 5 where the x's cancel out,

or you have l'Hopital's rule where lim_x->0 f(x)=0 but lim_x->0 f'(x) = 5

Answer 4

that first one should be lim_x->0 g(x) =5, I mistyped it.