lim x-> 0^- [abs(x)/x]

[kpx001]

how would i solve lim x-> 0^- [abs(x)/x] ? i dunno how to get x by itself or do problems with absolute values

 

[stapel]

how would i solve lim x-> 0^- [abs(x)/x] ?

A good start might be to draw the graph of f(x) = |x| / x. :idea:

i dunno how to get x by itself or do problems with absolute values

What do you mean by "getting x by itself"? You're taking a limit, not solving an equation! :shock:

To learn about absolute values and how to work with them (since we cannot teach the requested lessons nor draw the pictures here), try some of the online lessons that are available:

. . . . .Google results for "absolute value"

. . . . .Google results for "graph absolute value"

Note: I am assuming that "0^-" means "approaching zero from the left". When you reply, please confirm or correct. Thank you!

Eliz.

 

[kpx001]

yes its the approaching from left to right, and i know how absolute values work, im trying to solve it analytically, but i saw the graph in the graphing calculator (values of y from left to right = -1 from right to left = 1. its not a true limit but i dunno.

 

[galactus]

You're correct. It approaches -1 as x approaches 0 from the left. It approaches 1 as x approaches 0 from the right. Therefore, the two-sided limit doesn't exist.

If approaching from the left then x<0 and we have -x

So, -x/x = -1

 

[kpx001]

is there anyway to show analytically or is it just by plugging in?

 

[tkhunny]

How analytical do you want.

For x < 0, \(\displaystyle |x| = -x\)

For x < 0, \(\displaystyle \frac{|x|}{x}\;=\;\frac{-x}{x}\;=\;-1\)

I don't see any "plugging in" going on there.