A) 0
B) 1/2
C) 1
D) ?1
Correct Answer: C
Solution :
Multiply function by \[\frac{{{(1+x)}^{1/2}}+{{(1-x)}^{1/2}}}{{{(1+x)}^{1/2}}+{{(1-x)}^{1/2}}}\] and solve. Aliter : Apply L-Hospital?s rule, \[\underset{x\to 0}{\mathop{\lim }}\,\,\frac{{{(1+x)}^{1/2}}-{{(1-x)}^{1/2}}}{x}=\underset{x\to 0}{\mathop{\lim }}\,\,\frac{1}{2\sqrt{1+x}}+\frac{1}{2\sqrt{1-x}}=1\].
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