lim-x-pi-2-cos-2x-sin-3pi-2-x-

Question Number 130406 by john_santu last updated on 25/Jan/21

\lim_{x \to π / 2} \cos (2 x + \sin (\frac{3 π}{2} + x) = ?

Commented by Dwaipayan Shikari last updated on 25/Jan/21

- 1

Answered by EDWIN88 last updated on 25/Jan/21

\lim_{x \to a} f (g (x)) = f (\lim_{x \to a} g (x))

\lim_{x \to π / 2} \cos (2 x + \sin (\frac{3 π}{2} + x)) =

\cos (\lim_{x \to π / 2} (2 x + \sin (\frac{3 π}{2} + x)) =

\cos (π + \sin 2 π) = \cos π = - 1

Answered by mathmax by abdo last updated on 25/Jan/21

f (x) = \cos (2 x + \sin (\frac{3 π}{2} + x)) \Rightarrow f (x) = \cos (2 x + \sin (π + \frac{π}{2} + x))

= \cos (2 x - cosx) \Rightarrow \lim_{x \to \frac{π}{2}} f (x) = \cos (π - 0) = - 1