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## Homework Statement

[tex]\underset{x\rightarrow0}{\lim}\frac{x-xcosx}{sin^{2}3x}[/tex]

## Homework Equations

[tex]\sin ^{2}x = \frac{1-\cos 2x}{2}[/tex]

[tex]\frac{x}{\frac{y}{z}}=x\cdot \frac{z}{y}[/tex]

## The Attempt at a Solution

[tex]\underset{x\rightarrow0}{\lim}\frac{x-xcosx}{sin^{2}3x}[/tex]

[tex]=\underset{x\rightarrow0}{\lim}\frac{(x-x)cosx}{(\cfrac{1-cos(6x)}{2})}[/tex]

[tex]=\underset{x\rightarrow0}{\lim}\frac{(x-x)cosx}{1}\cdot\frac{2}{1-cos(6x)}[/tex]

[tex]=\underset{x\rightarrow0}{\lim}2((x-x)cosx)\cdot(1-cos(6x))[/tex]

[tex]=2((0)cos0)\cdot(1-cos0)[/tex]

[tex]=2(0\cdot1)\cdot(1-1)[/tex]

[tex]=0[/tex]