Question

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

Answer 1

\[\lim_{x \to 0^-} \left( \frac{\sin \left[ x \right]}{\left[ x \right]} \right)\]
\[ x = 0 - h\]
\[ \therefore h \to 0\]
\[ = \lim_{h \to 0} \left( \frac{\sin \left[ 0 - h \right]}{\left[ 0 - h \right]} \right)\]
\[ = \frac{\sin \left( - 1 \right)}{- 1}\]
\[ = \frac{- \sin 1}{- 1}\]
\[ = \sin 1\]