Question

$lim \: \: \sqrt{1 + x \: \: } - \: \sqrt{1 - x} \: \: \div \: x \\ x = 0$
a) -1
b) 1
c) 0
d) dose not exist​

Answer 1

Answer:

1

Step-by-step explanation:

$lim \: \frac{ \sqrt{1 + x } - \sqrt{1 - x} }{x}$

$lim \frac{ \sqrt{1 + x} - \sqrt{1 - x} }{x} \times \frac{ \sqrt{1 + x} + \sqrt{1 - x} }{ \sqrt{1 + x} + \sqrt{1 - x} }$

$lim \frac{1 + x -(1 - x)}{x \sqrt{1 + x} + x \sqrt{1 - x} }$

$lim \frac{2x}{x \sqrt{1 + x} + x \sqrt{1 - x} }$

$lim \frac{2}{ \sqrt{1 + x} + \sqrt{1 - x} }$

$\frac{2}{ \sqrt{1 + 0} + \sqrt{1 - 0} }$

$\frac{2}{ \sqrt{1} + \sqrt{1} }$

$\frac{2}{1 + 1}$

$\frac{2}{2} = 1$

Hope it helps you.

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