Another Limit problem :X

**greenbee** · September 20th 2009, 07:11 PM

Do x is NONE? Since 8/0 = undefined if I plug 0 into x? Agree? Just want to make sure. I am not good with math

Please give me a helping hand! Thank you!

**Chris L T521** · September 20th 2009, 07:17 PM

Originally Posted by greenbee

Do x is NONE? Since 8/0 = undefined if I plug 0 into x? Agree? Just want to make sure. I am not good with math

Please give me a helping hand! Thank you!

Recall that $\left|x\right|=\left\{\begin{array}{rl}x & x\geq 0\\ {\color{red}-x} & {\color{red}x<0}\end{array}\right.$

So in your case,

$\lim_{x\to0^-}\left(\frac{8}{x}-\frac{8}{\left|x\right|}\right)=\lim_{x\to0^-}\left(\frac{8}{x}+\frac{8}{x}\right)=\lim_{x\to 0^-}\frac{16}{x}$

I'm sure you can take it from here.

**greenbee** · September 20th 2009, 07:32 PM

Originally Posted by Chris L T521

Recall that $\left|x\right|=\left\{\begin{array}{rl}x & x\geq 0\\ {\color{red}-x} & {\color{red}x<0}\end{array}\right.$

So in your case,

$\lim_{x\to0^-}\left(\frac{8}{x}-\frac{8}{\left|x\right|}\right)=\lim_{x\to0^-}\left(\frac{8}{x}+\frac{8}{x}\right)=\lim_{x\to 0^-}\frac{16}{x}$

I'm sure you can take it from here.

Please tell me that it's 16?

**Prove It** · September 20th 2009, 07:42 PM

Originally Posted by greenbee

Please tell me that it's 16?

No, it's not 16.

Try graphing $f(x) = \frac{16}{x}$ and see what happens when $x \to 0$ from the left...

**greenbee** · September 20th 2009, 07:49 PM

Originally Posted by Prove It

No, it's not 16.

Try graphing $f(x) = \frac{16}{x}$ and see what happens when $x \to 0$ from the left...

It doesn't go to 0
It goes to like -Infinity
So the answer is -Infinity?

**Chris L T521** · September 20th 2009, 07:50 PM

Originally Posted by greenbee

It doesn't go to 0
It goes to like -Infinity
So the answer is -Infinity?

Yes, $\lim_{x\to0^-}\frac{16}{x}=-\infty$ .

**greenbee** · September 20th 2009, 07:52 PM

Originally Posted by Chris L T521

Yes, $\lim_{x\to0^-}\frac{16}{x}=-\infty$ .

YAY thank you so much!!!

(Thanks thanks thanks button)!!!

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