Question

lim(sin7x-sin5x)/(x^2+pix`)при x стремящийся 0. найти предел

Answer 1

$displaystyle lim_{x to 0} frac{sin 7x-sin 5x}{x^2+pi x}= lim_{x to 0} frac{sin 7x}{x(x+pi )} - lim_{x to 0} frac{sin 5x}{x(x+pi )}=\ \ \ = lim_{x to 0} frac{7}{x+pi} -lim_{x to 0} frac{5}{x+pi} =lim_{x to 0}frac{2}{x+pi}= frac{2}{ pi }$