Question

find the limit lim x→0 x^2 cos 1/x.

Answer 1

$\lim_{x\to0}(x^2*cos({\frac 1 x}))$

$\forall a:-1≤cos(a)≤1$

$\lim_{x\to0}x^2=0\implies \lim_{x\to0}(x^2*cos({\frac 1 x}))=0*b$ where $-1≤b≤1\implies \lim_{x\to0}(x^2*cos({\frac 1 x}))=0$