A) 1
B) ?1
C) 0
D) e
Correct Answer: A
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,\,\,{{(\cos x)}^{1/x}}=k\,\,\Rightarrow \,\,\underset{x\to 0}{\mathop{\lim }}\,\frac{1}{x}\log \,(\cos x)=\log k\] \[\Rightarrow \,\,\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{1}{x}\,\,\underset{x\to 0}{\mathop{\lim }}\,\,\,\log \,\cos x=\log k\] \[\Rightarrow \,\,\,\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{1}{x}\times 0={{\log }_{e}}k\,\,\Rightarrow \,k=1\] .
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