First slide

Introduction to limits

Question

If the value of $lim_{x \to 0} \frac{(1 - x)^{n} - 1}{x}$ is 100 , then $n =$

Moderate

A

100
B

-100
C

99
D

-99

Solution

We have,
$\begin{array}{l} lim_{x \to 0} \frac{(1 - x)^{n} - 1}{x} = 100 \\ = lim_{x \to 0} \frac{(1 - x)^{n} - 1^{n}}{(1 - x) - 1} = - 100 \\ = n (1)^{n - 1} = - 100 \Rightarrow n = - 100 \end{array}$

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