Question

lim стремится к 0 sin5x/tg2x

Answer 1

$lim_{n to inft0} frac{sin5x}{tg2x} = lim_{n to inft0} frac{sin5x}{ frac{sin2x}{cos2x} } = lim_{n to inft0} cos2xfrac{sin5x}{sin2x } = \ \ = lim_{n to inft0} cos2x * lim_{n to inft0} frac{sin5x}{sin2x } = 1*lim_{n to inft0} frac{sin5x}{sin2x } = \ \ = lim_{n to inft0} frac{ frac{sin5x}{x} }{ frac{sin2x}{x} } =lim_{n to inft0} frac{ frac{5 sin5x}{5x} }{ frac{2 sin2x}{2x} } = frac{5}{2} lim_{n to inft0} frac{ frac{sin5x}{5x} }{ frac{sin2x}{2x} } =$

$= frac{5}{2} frac{lim_{n to inft0} frac{sin5x}{5x} }{lim_{n to inft0} frac{sin2x}{2x} } = frac{5}{2} frac{1}{1} = frac{5}{2}$