First slide

Introduction to limits

Question

$If {Lim}_{x \to 5} \frac{x^{k} - 5^{k}}{x - 5} = 500, then the positive integral value of k is$

Moderate

A

3
B

4
C

5
D

6

Solution

$\begin{aligned} lim_{x \to 5} \frac{x^{k} - 5^{k}}{x - 5} = 500 \\ k \cdot 5^{k - 1} = 500 \\ \Rightarrow k 5^{k - 1} = {4.5}^{3} \\ k = 4 \end{aligned}$

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