Question

What is the vaue of ${lim}_{x\to \frac{\pi }{4}}\frac{cosx-sinx}{x-\frac{\pi }{4}}$

• A. $\sqrt{2}$
• B. 0
• C. -$\sqrt{2}$
• D. limit does not exist

Answer 1

The correct option is C -$\sqrt{2}$

${lim}_{x\to \pi /4}\frac{cosx-sinx}{x-\pi /4}\left(\frac{0}{0}form\right)$

= ${lim}_{x\to \pi /4}\frac{-sinx-cosx}{1}$

(using L- Hospital Rule)

= -$\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}=-\sqrt{2}$