calculate-lim-x-pi-4-sin-2x-sin-x-pi-4-sinx-cosx-

Question Number 42781 by maxmathsup by imad last updated on 02/Sep/18

c a l c u l a t e {l i m}_{x \to \frac{π}{4}} \frac{s i n (2 x) s i n (x - \frac{π}{4})}{s i n x - c o s x}

Commented by maxmathsup by imad last updated on 04/Oct/18

l e t A (x) = \frac{s i n (2 x) s i n (x - \frac{π}{4})}{s i n x - c o s x} w e h a v e A (x) = \frac{s i n (2 x) s i n (x - \frac{π}{4})}{\sqrt{2} s i n (x - \frac{π}{4})}

\Rightarrow {l i m}_{x \to \frac{π}{4}} A (x) = {l i m}_{x \to \frac{π}{4}} \frac{s i n (2 x)}{\sqrt{2}} = \frac{1}{\sqrt{2}} .

Answered by tanmay.chaudhury50@gmail.com last updated on 03/Sep/18

l i \underset{x \to \frac{Π}{4}}{m} \frac{s i n 2 x \times \frac{1}{\sqrt{2}} (s i n x - c o s x)}{s i n x - c o s x}

= \frac{1}{\sqrt{2}} \times s i n \frac{Π}{2} = \frac{1}{\sqrt{2}}

\lim_{t \to 0}

\underset{t \to 0}{li}