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$$
\lim _{x \rightarrow 0} \frac{\tan ^4 x-\sin ^4 x}{x^6}=
$$
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\lim _{x \rightarrow 0} \frac{\tan ^4 x-\sin ^4 x}{x^6}=
$$
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2039 Upvotes
Verified Answer
The correct answer is:
2
$\begin{aligned} & \text {} \lim _{x \rightarrow 0} \frac{\tan ^4 x-\sin ^4 x}{x^6}=\lim _{x \rightarrow 0} \frac{\sin ^4 x\left(\sec ^4 x-1\right)}{x^6} \\ & =\lim _{x \rightarrow 0} \frac{\sin ^4 x}{x^4} \cdot \frac{\tan ^2 x}{x^2} \times\left(\sec ^2 x+1\right) \\ & =1 \times 1 \times 2=2 .\end{aligned}$
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