Question

Помогите пожалуйста, очень срочно!! 59-66

Answer 1

59.$lim_{x to 0} frac{sin7x}{x} = lim_{x to 0} 7* frac{sin7x}{7x} = 7*1 = 7$
60.$lim_{x to 0} frac{sin8x}{x} = lim_{x to 0} 8* frac{sin8x}{8x} = 8*1 = 8$
61.$lim_{x to 0} frac{sin2 x^{2} }{ x^{2}} = lim_{x to 0}2* frac{sin2 x^{2} }{ 2x^{2}} = 2*1 = 2$
62.$lim_{x to 0} frac{sin3x}{sin5x} = lim_{x to 0} frac{3}{5} frac{sin3x * 5x}{3x*sin5x} = frac{3}{5} *1*1 = frac{3}{5}$
63.$lim_{x to 0} frac{(sinx)^{2} }{ x^{2}} = lim_{x to 0}frac{sinx*sinx} {x*x} = 1*1 = 1$
64.$lim_{x to 0} frac{sinx}{tg3x} = lim_{x to 0} frac{sinx * cos3x}{sin3x} = lim_{x to 0}frac{1}{3} frac{3x*sinx * cos3x}{sin3x*x}$
$= frac{1}{3}*1*1*1 = frac{1}{3}$
65.$lim_{x to 0} frac{sin3x}{sin4x} = lim_{x to 0} frac{3}{4} frac{sin3x * 4x}{3x*sin4x} = frac{3}{4} *1*1 = frac{3}{4}$
66.$lim_{x to 0} xctgx = lim_{x to 0} frac{x*cosx}{sinx} = 1*1=1$