A) \[4\sqrt{2}\]
B) \[8\sqrt{2}\]
C) 4
D) 8
Correct Answer: D
Solution :
\[\underset{x\to \frac{\pi }{4}}{\mathop{\lim }}\,\frac{{{\cot }^{3}}x-\tan x}{\cos \left( x+\frac{\pi }{4} \right)}\] \[=\underset{x\to \frac{\pi }{4}}{\mathop{\lim }}\,\frac{1-{{\tan }^{4}}x}{\cos \left( x+\frac{\pi }{4} \right)}=2\underset{x\to \frac{\pi }{4}}{\mathop{\lim }}\,\frac{1-{{\tan }^{2}}x}{\cos \left( x+\frac{\pi }{4} \right)}\] \[=2\underset{x\to \frac{\pi }{4}}{\mathop{\lim }}\,\frac{{{\cos }^{2}}x-{{\sin }^{2}}x}{\frac{1}{\sqrt{2}}(\cos \,x-\sin x)}.\frac{1}{{{\cos }^{2}}x}\] \[=4\sqrt{2}\,\,\,\underset{x\to \frac{\pi }{4}}{\mathop{\lim }}\,(\cos \,x+\sin x)=8\]
You need to login to perform this action.
You will be redirected in
3 sec
