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Write the Value of Lim X → 0 − Sin [ X ] [ X ] . - Mathematics

Answer in Brief

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

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Solution

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

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