granica funkcji

[ania2132]

lim (|sinx|^3)/x
x->0

[ewelawwy]

\(\lim_{x\to 0} \frac{|\sin x|^3}x=\[\frac 00\] =^H \lim_{x\to 0} \frac {3\sin x\sqrt{\sin ^2x}\cos x}{1}=0\)

[octahedron]

\(\lim_{x\to 0^+}\frac{|\sin x|}{x}=\lim_{x\to 0^+}\frac{\sin x}{x}=1
\lim_{x\to 0^-}\frac{|\sin x|}{x}=\lim_{x\to 0^-}-\frac{\sin x}{x}=-1
\lim_{x\to 0}\sin^2x=0
\lim_{x\to 0}\frac{|\sin x|^3}{x}=\lim_{x\to 0}\sin^2x\cdot\frac{|\sin x|}{x}=0\)