Question

Limit (x --> 0) (sin 2x + sin 6x)/(sin 5x - sin 3x)

Answer 1

use concept ,

Lim(f(x)→0) {sinf(x)/f(x)}

when, f(x) →0
and sinf(x) →0

then, Lim f(x)→0 sinf(x)/f(x) = 1

now,

Lim(x→0) {sin2x/2x(2x) + sin6x/6x(6x)}/{sin5x/5x(5x) -sin3x/3x(3x)}

Lim(x→0){2x +6x}/{5x -3x} = Lim(x→0){8x/2x}

=4