First slide

Introduction to limits

Question

$Let f : R \to [0, \infty] be such that lim_{x \to 5} f (x) exists and lim_{x \to 5} \frac{(f (x))^{2} - 9}{\sqrt{| x - 5 |}} = 0 then$ $lim_{x \to 5} f (x) equals$

Moderate

A

0
B

1
C

2
D

3

Solution

$\begin{aligned} lim_{x \to 5} \frac{[f (x)]^{2} - 9}{\sqrt{| x - 5 |}} = 0 \\ \Rightarrow lim_{x \to 5} [(f (x))^{2} - 9] = 0 \\ \Rightarrow lim_{x \to 5} f (x) = 3 \end{aligned}$

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