Which one of the following limit does not have value unity?

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Which one of the following limit does not have value unity? (a) lim⁡x→0sin⁡(tan⁡x)sin⁡x\lim_{x \rightarrow 0} \frac{\sin(\tan x)}{\sin x} (b) lim⁡x→π2sin⁡(cos⁡x)cos⁡x\lim_{x \rightarrow \frac{\pi}{2}} \frac{\sin(\cos x)}{\cos x} (c) lim⁡x→01+x−1−xx\lim_{x \rightarrow 0} \frac{\sqrt{1+x} - \sqrt{1-x}}{x} (d) lim⁡x→0(sin⁡xx)1x2\lim_{x \rightarrow 0} \left( \frac{\sin x}{x} \right)^{\frac{1}{x^2}}

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