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Question Number 72071 by aliesam last updated on 23/Oct/19

$$a)\underset{x\to 0}{lim}\frac{3x-sin\left(2x\right)}{2x-sin\left(3x\right)}$$$$$$$$$$

Commented by mathmax by abdo last updated on 24/Oct/19

$$sin\left(2x\right)\sim 2xandsin\left(3x\right)\sim 3x(x\to 0)\Rightarrow \frac{3x-sin\left(2x\right)}{2x-sin\left(3x\right)}\sim \frac{3x-2x}{2x-3x}$$$$\sim -1\Rightarrow {lim}_{x\to 0}\frac{3x-sin\left(2x\right)}{2x-sin\left(3x\right)}=-1$$

Answered by Tanmay chaudhury last updated on 23/Oct/19

$$\underset{x\to 0}{\lim }\frac{3-\left(\frac{sin2x}{2x}\right)\times 2}{2-\left(\frac{sin3x}{3x}\right)\times 3}$$$$=\frac{3-1\times 2}{2-1\times 3}=-1$$

Answered by malwaan last updated on 24/Oct/19

$$\underset{\mathit{x}\to 0}{\mathit{l}\mathit{i}\mathit{m}}\frac{3\mathit{x}-\mathit{s}\mathit{i}\mathit{n}\left(2\mathit{x}\right)}{2\mathit{x}-\mathit{s}\mathit{i}\mathit{n}\left(3\mathit{x}\right)}=\frac{3-2}{2-3}=-1$$

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