A) \[a\]
B) \[2a\]
C) \[\frac{a}{2}\]
D) \[4a\]
Correct Answer: C
Solution :
[c] We have \[\underset{x\to \infty }{\mathop{\lim }}\,{{2}^{x-1}}\tan \left( \frac{a}{{{2}^{x}}} \right)=\underset{x\to \infty }{\mathop{\lim }}\,\frac{a}{2}\frac{\tan \left( \frac{a}{{{2}^{x}}} \right)}{\left( \frac{a}{{{2}^{x}}} \right)}\left( \frac{0}{0}form \right)\] \[=\frac{a}{2}\underset{y\to 0}{\mathop{\lim }}\,\frac{\tan y}{y}=\frac{a}{2}\] \[\left( where\,\,y=\frac{a}{{{2}^{x}}} \right)\]
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