Question

Вычислить предел

1. $lim_{x to 0} frac{2sin5x}{8x}$
2. $lim_{x to 0 } frac{3x-sin2x}{sinx}$

Answer 1

$lim_{x to 0} frac{2 sin(5x) }{8x} = lim_{x to 0}( frac{ sin(5x) }{4x} )' = \ = lim_{x to 0} frac{5 cos(5x) }{4} = frac{5 cos(0) }{4} = frac{5}{4}$

$lim_{x to 0} frac{3x - sin(2x) }{ sin(x) } = lim_{x to 0}( frac{3x - sin(2x) }{ sin(x) } )' = \ = lim_{x to 0} frac{3 - 2 cos(2x) }{ cos(x) } = frac{3 - 2}{1} = 1$