Question

$\underset{\alpha \to \frac{\pi }{4}}{lim}\frac{\sin \alpha -\cos \alpha }{\alpha -\frac{\pi }{4}}=$

• A. $\sqrt{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. $1$
• D. None of these

Answer 1

The correct option is A $\sqrt{2}$

${lim}_{\alpha \to \pi /4}\frac{\sin \alpha -\cos \alpha }{\alpha -\frac{\pi }{4}}$

Since $0/0$ (indeterminate form)

$={lim}_{\alpha \to \pi /4}\frac{\cos \alpha +\sin \alpha }{1}$

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