Question

lim(cos(4x)-cos^3(4x))/(3x^2)
х стремится к 0

Answer 1

$limlimits _{x to 0}frac{cos4x-cos^34x}{3x^2}=limlimits _{x to 0}frac{cos4xcdot (1-cos^24x)}{3x^2}=limlimits _{x to 0}frac{cos4xcdot sin^24x}{3x^2}=\\=Big [; sinasim a; ,; ato 0; ; Rightarrow ; ; 4xto 0; ,; sin4xsim 4x; Big ]=limlimits _{x to 0}frac{cos4xcdot (4x)^2}{3x^2}=\\=limlimits _{x to 0}frac{cos4xcdot 16x^2}{3x^2}=limlimits _{x to 0}frac{cos4xcdot 16}{3}=Big [; cos0=1; Big ]=frac{1cdot 16}{3}=frac{16}{3}$

Answer 2

Ничего не понятно