A) \[1\]
B) \[-\frac{1}{2}\]
C) \[\frac{1}{2\sqrt{2}}\]
D) \[\frac{1}{2}\]
Correct Answer: D
Solution :
\[\underset{x\to \pi /4}{\mathop{\lim }}\,\frac{\sqrt{2}\,\cos x-1}{\cos \,x-1}\] \[\left( \frac{0}{0}form \right)\] \[\underset{x\to \pi /4}{\mathop{\lim }}\,\frac{-\sqrt{2}sinx-0}{-\text{cose}{{\text{c}}^{2}}x-0}\] (using L? Hospital?s rule) \[=\underset{x\to \pi /4}{\mathop{\lim }}\,\,\,\sqrt{2}\,{{\sin }^{3}}x\] \[=\sqrt{2}\times {{\left( \frac{1}{\sqrt{2}} \right)}^{3}}=\frac{1}{2}\]
You need to login to perform this action.
You will be redirected in
3 sec
