Question 134

$$\lim_{x \rightarrow 0}\frac{\sqrt{1 + x} - \sqrt{1 - x}}{x}$$

Solution

Multiplying numerator and denominator by $$\sqrt{\ 1+x}+\sqrt{\ 1-x}$$, we get:

$$\lim\ x\longrightarrow\ 0\ $$ $$\frac{\left(1+x\right)-\left(1-x\right)}{x\cdot\left(\sqrt{\ 1+x}+\sqrt{\ 1-x}\right)}$$
$$=\frac{2}{\left(\sqrt{\ 1+x}+\sqrt{\ 1-x}\right)}$$

Putting x = 0 now, we get

Result = 2/2 = 1

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AP ICET 2nd May 2018 Shift-2

$$\lim_{x \rightarrow 0}\frac{\sqrt{1 + x} - \sqrt{1 - x}}{x}$$

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