Q103 / 160 · TS EAMCET 2023 (13 May Shift 2) · Mathematics

$$ \lim _{x \rightarrow 0} \frac{\tan ^4 x-\sin ^4 x}{x^6}= $$

  • A
    $\frac{1}{2}$
  • B
    $\frac{5}{2}$
  • Correct answer
    C
    2
  • D
    4

Solution

$\begin{aligned} & \text {} \lim _{x \rightarrow 0} \frac{\tan ^4 x-\sin ^4 x}{x^6}=\lim _{x \rightarrow 0} \frac{\sin ^4 x\left(\sec ^4 x-1\right)}{x^6} \\ & =\lim _{x \rightarrow 0} \frac{\sin ^4 x}{x^4} \cdot \frac{\tan ^2 x}{x^2} \times\left(\sec ^2 x+1\right) \\ & =1 \times 1 \times 2=2 .\end{aligned}$

Hence, the correct answer is option: 'C'.

Relevant Questions