A) 1
B) -1
C) 0
D) None of these
Correct Answer: A
Solution :
[a] \[\underset{h\to 0}{\mathop{\lim }}\,\left[ \cos e{{c}^{3}}x.\cot x-2{{\cot }^{3}}x.\cos ecx+\frac{{{\cot }^{4}}x}{\sec x} \right]\] \[=\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{\cos x}{{{\sin }^{4}}x}-\frac{2{{\cos }^{3}}x}{{{\sin }^{4}}x}+\frac{{{\cos }^{5}}x}{{{\sin }^{4}}x} \right)\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{\cos x{{(1-co{{s}^{2}}x)}^{2}}}{{{\sin }^{4}}x}=\underset{x\to 0}{\mathop{\lim }}\,\cos x=1.\]
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