Question

please solve this pleaaaaaaaaaaaaaaaasssssee​

Answer 1

Step-by-step explanation:

$\lim_{x \rarr0} \frac{ \cos(9x) - \cos(5x) }{ \sin(17x) - \sin(3x) }$

$= \lim_{ x\rarr0} \frac{ - 2 \sin(7x) \sin(2x) }{2 \cos(10x) \sin(7x) }$

$= - \lim_{ x\rarr0} \frac{ \sin(2x) }{\cos(10x) }$

$= - \lim_{ x\rarr0} \frac{ \sin(2x) }{2x} \times \frac{2x}{ \cos(10x) }$

$= - \lim_{ 2x\rarr0} \frac{ \sin(2x) }{2x} \times \lim_{ x\rarr0} \frac{2x}{ \cos(2x) }$

$= - 1 \times 0$

$= 0$