Limits & Continuity: The value of lim_xto0 (fracxsqrt[8]1-sin x-sqrt[8]1+sin x ) is equal… | JEE Main 2021 | Yukti Vault

Yukti Vault

JEE Main 2021 (Online) 27th July Evening ShiftQuestion 1

The value of $\lim_{x\to0}\left(\frac{x}{\sqrt[8]{1-\sin x}-\sqrt[8]{1+\sin x}}\right)$ is equal to :

Limits & Continuity

$0$$-1$$-4$✓ Correct answer$4$

Solution

$(1\mp\sin x)^{1/8}\approx1\mp\frac{\sin x}8$, so denominator $\approx-\frac{\sin x}4\approx-\frac x4$. Limit $=-4$. Option (C).

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