Evaluate the following limits: _ x 2 [ x^ -3 -2^ -3 x-2 ] - Vidyadip

Question

Evaluate the following limits:

$\lim _{x \rightarrow 2}\left[\frac{x^{-3}-2^{-3}}{x-2}\right]$

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Answer

$\begin{aligned} \lim _{x \rightarrow 2} \frac{x^{-3}-2^{-3}}{x-2} & =(-3) \cdot(2)^{-4} \\ & \ldots\left[\because \lim _{x \rightarrow a} \frac{x^n-\mathrm{a}^{\mathrm{n}}}{x-\mathrm{a}}=\mathrm{na}^{\mathrm{n}-1}\right] \\ & =-3 \times \frac{1}{2^4} \\ & =\frac{-3}{16} \text { }\end{aligned}$

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