Differentiation Question 198
Question: Evaluate $ \underset{x\to \infty }{\mathop{\lim }}{2^{x-1}}\tan ( \frac{a}{2^{x}} ). $
Options:
A) $ a $
B) $ 2a $
C) $ \frac{a}{2} $
D) $ 4a $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] We have $ \underset{x\to \infty }{\mathop{\lim }}{2^{x-1}}\tan ( \frac{a}{2^{x}} )=\underset{x\to \infty }{\mathop{\lim }}\frac{a}{2}\frac{\tan ( \frac{a}{2^{x}} )}{( \frac{a}{2^{x}} )}( \frac{0}{0}form ) $
$ =\frac{a}{2}\underset{y\to 0}{\mathop{\lim }}\frac{\tan y}{y}=\frac{a}{2} $
$ ( wherey=\frac{a}{2^{x}} ) $
BETA
