why does lim (x/|x|) = 1

x-> 0+

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- Jul 28th 2009, 06:59 PMricey[SOLVED] limits
why does lim (x/|x|) = 1

x-> 0+ - Jul 28th 2009, 07:09 PMVonNemo19
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 $\displaystyle |x|=\left\{\begin{array}{cc}{-x},&\mbox{ if }{x}\leq0\\x,&\mbox{ if }{x>0}\end{array}\right.$

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

Therefore $\displaystyle \lim_{x\to0^+}\frac{x}{|x|}=\lim_{x\to0^+}\frac{x} {x}=\lim_{x\to0^+}(1)=1$. - Jul 28th 2009, 08:05 PMricey
okay i get it! Thanks so much