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Question: Answered & Verified by Expert
$$
\lim _{x \rightarrow 0} \frac{\tan ^4 x-\sin ^4 x}{x^6}=
$$
MathematicsLimitsTS EAMCETTS EAMCET 2023 (13 May Shift 2)
Options:
  • A $\frac{1}{2}$
  • B $\frac{5}{2}$
  • C 2
  • D 4
Solution:
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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