Question

if the lim x->0 f(x)/(x^2) = 8 then
lim x->0 f(x) =
and
lim x->0 f(x)/x =

Answer 1

The limit of \(f(x)\) as \(x\to 0\) must be zero. Otherwise the limit of \(f(x)/x^2\) is undefined.
\(\lim f(x)/x=\lim f(x)/x^2\lim x=8\cdot 0=0\) (all the limit approaches 0)

Answer 2

or in other words lim x->0 f(x)=8*x^2=0 and
lim x->0 f(x)/x= lim(8*x^2)/x =lim 8x =0, as x->0