Question

evaluate the limit: x->0 (x^2)*sin(1/x)

Answer 1

lim x->0 x* sin(1/x)/(1/x) = 0 * 1 = 0

Answer 2

\[\lim_{x \rightarrow 0}\left(x^{2}\sin \left( \frac{1}{x} \right)\right)\left( \frac{\frac{1}{x}}{\frac{1}{x}} \right)\]\[=\lim_{x \rightarrow 0}\left( \frac{x \sin \left( \frac{1}{x} \right)}{\frac{1}{x}} \right)=\left( 0 \right)\left( 1 \right)=0\]

Answer 3

to be exact it's rather like this

lim x->0 x * lim x->0 sin(1/x)/(1/x) = 0 * 1 = 0