Question

$\underset{a\to \pi /4}{lim}\frac{\sin \alpha -\cos \alpha }{\alpha -\pi /4}.$ is $\sqrt{b}$ Find b

Answer 1

$\underset{a\to \pi /4}{lim}\frac{\sin \alpha -\cos \alpha }{\alpha -\pi /4},\left(\frac{0}{0}\right)$ form

So using L -Hospital's rule,

$\underset{a\to \pi /4}{lim}\frac{\cos \alpha +\sin \alpha }{1}=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}=\sqrt{2}$

$\Rightarrow b=2$