# Math Help - Trig Limit

1. ## Trig Limit

$\lim_{x\to1^{-1}}(x-1) sin(\frac{1}{x-1})$

I heard that the answer equals 0, if so how is this?

thank you

2. Let $t=x-1$ to get $\lim_{t\to 0}t\sin \frac{1}{t}$.

Note, $\left| \sin \frac{1}{t}\right|\leq 1$ use squeeze theorem.