Question

Помогите,пожалуйста! №

Answer 1

$limlimits _{xto 0}frac{sinx}{x}=1; ;; ; limlimits _{alpha (x)to 0}frac{sin, alpha (x)}{alpha (x)}=1\\\ limlimits _{x to 0}frac{sin7x}{x}=limlimits _{xto 0}(frac{sin7x}{7x}cdot 7)=1cdot 7=7\\limlimits _{xto 0} frac{sin2x^2}{x^2} =limlimits _{xto 0}(frac{sin2x^2}{2x^2}cdot 2)=1cdot 2=2\\limlimits _{xto 0} frac{sin^2x}{x^2} =limlimits _{xto 0}(frac{sinx}{x}cdot frac{sinx}{x})=1cdot 1=1$

$limlimits _{xto 0} frac{sin3x}{sin4x} =limlimits _{xto 0} (frac{sin3x}{3x} cdot 3xcdot frac{4x}{sin4x} cdot frac{1}{4x})=limlimits _{xto 0} frac{3x}{4x} =frac{3}{4}$