[SOLVED] limits

**ricey** · July 28th 2009, 06:59 PM

why does lim (x/|x|) = 1
x-> 0+

**VonNemo19** · July 28th 2009, 07:09 PM

Originally Posted by ricey

why does lim (x/|x|) = 1
x-> 0+

It does because we are only concerned about the behavior of the graph from the right, IE: (positive values of x)

Note how any positive number divided by the absolute value of that number will always be positve 1.

Since $|x|=\left\{\begin{array}{cc}{-x},&\mbox{ if }{x}\leq0\\x,&\mbox{ if }{x>0}\end{array}\right.$

Then for values greater than 0, we have $\frac{x}{|x|}=\frac{x}{x}$

Therefore $\lim_{x\to0^+}\frac{x}{|x|}=\lim_{x\to0^+}\frac{x} {x}=\lim_{x\to0^+}(1)=1$ .

**ricey** · July 28th 2009, 08:05 PM

okay i get it! Thanks so much

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