Functions Question 248
Question: $ \underset{x\to \pi /2}{\mathop{\lim }},\frac{{a^{\cot x}}-{a^{\cos x}}}{\cot x-\cos x}= $
[Kerala (Engg.) 2001; J & K 2005]
Options:
A) $ \log a $
B) $ \log 2 $
C) a
D) log x
Show Answer
Answer:
Correct Answer: A
Solution:
$ \underset{x\to \pi /2}{\mathop{lim}}( \frac{{a^{\cot x}}-{a^{\cos x}}}{\cot x-\cos x} ) $ $ =\underset{x\to \pi /2}{\mathop{lim}},{a^{\cos x}}( \frac{{a^{\cot x-\cos x}}-1}{\cot x-\cos x} ) $ $ ={a^{\cos (\pi /2)}}\underset{x\to \pi /2}{\mathop{lim}},( \frac{{a^{\cot x-\cos x}}-1}{\cot x-\cos x} ) $ $ =1.\log a=\log a $ .
BETA
