[SOLVED] limits

Quote:

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