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  • Choose the correct answer out of 4 options given against each Question 〖lim〗┬(x→0) (sin⁡x/(√(x+1)-√(1-x))) is A. 2

Choose the correct answer out of 4 options given against each Question

\mathop{\lim }_{x \rightarrow 0} \left( \frac{\sin x}{\sqrt {x+1}-\sqrt {1-x}} \right)  is

A. 2
B. 0
C. 1
D. –1

Answers (1)

\\ \mathop{\lim }_{x \rightarrow 0} \left( \frac{\sin x}{\sqrt {x+1}-\sqrt {1-x}} \right) \\ \\ =\mathop{\lim }_{x \rightarrow 0} \left( \frac{\sin x \left( \sqrt {x+1}+\sqrt {1-x} \right) }{ \left( \sqrt {x+1}-\sqrt {1-x} \right) \left( \sqrt {x+1}+\sqrt {1-x} \right) } \right) \\ \\ =\mathop{\lim }_{x \rightarrow 0} \left( \frac{\sin x \left( \sqrt {x+1}+\sqrt {1-x} \right) }{ \left( x+1-1+x \right) } \right) \\ \\ =\mathop{\lim }_{x \rightarrow 0} \left( \frac{\sin x \left( \sqrt {x+1}+\sqrt {1-x} \right) }{2x} \right) \\ \\ =1 \\ \\

Hence, the answer is option C

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