Question

Write the value of ${lim}_{x\to 0^{-}}\frac{\sin \left[x\right]}{\left[x\right]}.$

Answer 1

${lim}_{x\to 0^{-}}\frac{\sin \left[x\right]}{\left[x\right]}={lim}_{h\to 0}\frac{\sin [0-h]}{[0-h]}={lim}_{h\to 0}\frac{\sin (-1)}{-1}=-\frac{sin\left(1\right)}{-1}{lim}_{x\to 0^{-}}\frac{sin\left[x\right]}{\left[x\right]}=\sin \left(1\right)$