First slide

Introduction to limits

Question

The value of $lim_{x \to 0} \frac{\sqrt{x^{2} + 1} - 1}{\sqrt{x^{2} + 9} - 3}$ , is

Moderate

A

3
B

4
C

1
D

2

Solution

we have,
$\begin{array}{l} lim_{x \to 0} \frac{\sqrt{x^{2} + 1} - 1}{\sqrt{x^{2} + 9} - 3} = lim_{x \to 0} \frac{x^{2} + 1 - 1}{x^{2} + 9 - 9} \times \frac{\sqrt{x^{2} + 9} + 3}{\sqrt{x^{2} + 1} + 1} \\ = lim_{x \to 0} \frac{\sqrt{x^{2} + 9} + 3}{\sqrt{x^{2} + 1} + 1} = \frac{6}{2} = 3 \end{array}$

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