* $\mathop {\lim }\limits_{x \to 0}(\frac{x-sinx}{x^2.sinx})=\mathop {\lim }\limits_{x \to 0}(\frac{1-cosx}{2xsinx+x^2cosx})=\mathop {\lim }\limits_{x \to 0}(\frac{x^2}{2x^2(2\frac{sinx}{x}+cosx)})=\frac{1}{6}$* $\mathop {\lim }\limits_{x \to 0}(\frac{x-(x-\frac{x^3}{3!}+\theta (x^3))}{x^3})=\frac{1}{6}$
* $\mathop {\lim }\limits_{x \to 0}(\frac{x-
\sin
x}{x^2.
\sin
x})=\mathop {\lim }\limits_{x \to 0}(\frac{1-
\cos
x}{2x
\sin
x+x^2
\cos
x})=\mathop {\lim }\limits_{x \to 0}(\frac{x^2}{2x^2(2\frac{
\sin
x}{x}+
\cos
x)})=\frac{1}{6}$* $\mathop {\lim }\limits_{x \to 0}(\frac{x-(x-\frac{x^3}{3!}+\theta (x^3))}{x^3})=\frac{1}{6}$