Lim sin8x+sin2xx-0. 4xcos3x

Lim sin8x+sin2xx-0. 4xcos3x

$lim_{x to0} frac{ sin(8x) + sin(2x) }{4x cos(3x) } \ = lim_{x to0} frac{2 sin( frac{8 + 2}{2} x) cos( frac{8 - 2}{2} x) }{4x cos(3x) } \ = lim_{x to0} frac{2 sin(5x) cos(3x) }{4x cos(3x) } \ = lim_{x to0} frac{2 sin(5x) }{4x} \ = frac{1}{2} lim_{x to0} frac{ sin(5x) }{x} \ = frac{5}{2}$