Differentiation Question 484
Question: $ \underset{x\to 0}{\mathop{\lim }},[ \cos ec^{3}x.\cot x-2{{\cot }^{3}}x.\cos ecx+\frac{{{\cot }^{4}}x}{\sec x} ] $ is equal to
Options:
1
-1
0
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \underset{h\to 0}{\mathop{\lim }},[ \cos ec^{3}x.\cot x-2{{\cot }^{3}}x.\cos ecx+\frac{{{\cot }^{4}}x}{\sec x} ] $ $ =\underset{x\to 0}{\mathop{\lim }},( \frac{\cos x}{{{\sin }^{4}}x}-\frac{2{{\cos }^{3}}x}{{{\sin }^{4}}x}+\frac{{{\cos }^{5}}x}{{{\sin }^{4}}x} ) $ $ =\underset{x\to 0}{\mathop{\lim }},\frac{\cos x{{(1-{{\cos }^{2}}x)}^{2}}}{{{\sin }^{4}}x}=\underset{x\to 0}{\mathop{\lim }},\cos x=1. $
BETA
