# Find left limit $\lim\limits_{x \to{}0}{\frac{-\sin|x|}{x}}$

I have a little confusion with signs. Thanks in advance.

$$\lim_{x \to 0^-}{\frac{-\sin|x|}{x}}$$ (This is a left limit, i.e. $x<0$)

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What is $sen{}$? –  Chris Eagle Dec 2 '12 at 16:51
@ChrisEagle It's $\sin$ in spanish (seno). –  Pragabhava Dec 2 '12 at 16:52
It's already edited, thanks for a while. –  Rakisbro Dec 2 '12 at 16:53
Do you mean $\lim_{x\to 0^-}$ when you say left limit? –  Asaf Karagila Dec 2 '12 at 16:54
that's that I mean Asaf. –  Rakisbro Dec 2 '12 at 17:00

$$x<0\Longrightarrow |x|=-x\Longrightarrow\frac{-\sin|x|}{x}=\frac{\sin x}{x}\xrightarrow [x\to 0^-]{}1$$

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sorry for the dumb question but ... $$sin(-x) = -sin(x)$$ is it correct? –  Rakisbro Dec 2 '12 at 17:04
Si, claro: el seno es una función impar....Yes, of course: sine is an odd function. –  DonAntonio Dec 2 '12 at 17:06
I see, thanks for the courtesy. –  Rakisbro Dec 2 '12 at 17:09