A) \[\log x\]
B) 1
C) 0
D) \[-\log \frac{1}{a}\]
Correct Answer: D
Solution :
\[\underset{x\to \infty }{\mathop{\lim }}\,x\,({{a}^{1/x}}-1)=\underset{x\to \infty }{\mathop{\lim }}\,\,\left[ \frac{{{a}^{1/x}}-1}{1/x} \right]\] \[=\underset{x\to \infty }{\mathop{\lim }}\,\frac{[{{e}^{{{\log }_{e}}{{a}^{1/x}}}}-1]}{1/x}={{\log }_{e}}a=-{{\log }_{e}}\frac{1}{a}.\]
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