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Take the limit of (sin(x-4))/(tan(x^2 - 16) as x approaches 4.

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Answer to a math question Take the limit of (sin(x-4))/(tan(x^2 - 16) as x approaches 4.

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Adonis

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$\lim_{x \rightarrow 4} \left(\frac{ \frac{ \mathrm{d} }{ \mathrm{d}x} \left( \sin\left({x-4}\right) \right) }{ \frac{ \mathrm{d} }{ \mathrm{d}x} \left( \tan\left({{x}^{2}-16}\right) \right) }\right)$

$\lim_{x \rightarrow 4} \left(\frac{ \cos\left({x-4}\right) }{ \frac{ \mathrm{d} }{ \mathrm{d}x} \left( \tan\left({{x}^{2}-16}\right) \right) }\right)$

$\lim_{x \rightarrow 4} \left(\frac{ \cos\left({x-4}\right) }{ 2x \times {\sec\left({{x}^{2}-16}\right)}^{2} }\right)$

$\frac{ \cos\left({4-4}\right) }{ 2 \times 4{\sec\left({{4}^{2}-16}\right)}^{2} }$

$\begin{align*}&\frac{ 1 }{ 8 } \\&\begin{array} { l }0.125,& {2}^{-3}\end{array}\end{align*}$

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