Question

limite cuando x tiende a 0 de x - a / sen(4x) - sen(4a) urgente xf

Answer 1

$L=\lim\limits_{x\to 0}\dfrac{x-a}{\sin 4x-\sin 4a}\\ \\ \\ L=\lim\limits_{x\to 0}\dfrac{x-a}{-2\cos(4x+4a)\sin(4x-4a)}\\ \\ \\ L=\lim\limits_{x\to 0}\dfrac{4x-4a}{-8\cos(4x+4a)\sin(4x-4a)}\\ \\ \\ L=-\dfrac{1}{8}\lim\limits_{x\to 0}\dfrac{4x-4a}{\sin(4x-4a)}\cdot \dfrac{1}{\cos(4x+4a)}\\ \\ \\ \boxed{L=-\dfrac{1}{8}}$