# Homework Help: Need a little help please.

1. Jun 22, 2005

### naicidrac

Hello everybody. I just need a little help with some very basic Calculus. Actually I need help with the Algebra part, but it is a Calculus problem. Here is the problem.
Lim x->-2 of (x^2+3x+2)/(2-|x|)

That is it and I know the answer is -1, but I cannot get that |x| out of the denomenator, I have tried to multiply by the conjugate, but that did not seem to work. Thanks in andave for any advice.

Last edited: Jun 22, 2005
2. Jun 22, 2005

### wisredz

Is it x^2+3x+2 or x^2+3x-2?

3. Jun 22, 2005

### Vegeta

He must mean
$$\lim_{x\rightarrow -2}\frac{x^2+3x+2}{2-|x|}$$
Otherwise it's undefined.

4. Jun 22, 2005

### naicidrac

I edited my post and Vegeta was correct.

5. Jun 22, 2005

### AKG

As x approaches -2, x is negative.

6. Jun 22, 2005

### whozum

Think of the absolute value funciton as a piecewise function, defined separately for positive numbers and negative numbers.

7. Jun 22, 2005

### wisredz

Yes and keep in my to factor x^2+3x+2

8. Jun 22, 2005

### naicidrac

I have thought of it as a piecewise function, but my instructions are to solve this algebraically. I have also factored it ((x+1)(x+2))/(2-|x|). Now what? Thanks for the help.

9. Jun 22, 2005

### whozum

Defining piecewise functions is an algebraic method.

10. Jun 22, 2005

### wisredz

As you approach -2 from left and right, lxl is defined as -x. Try to use this.

11. Jun 23, 2005

### keeti

x is having the negative value in this case then IxI will have I-2I=-2
so the 2-IXI term will be 4 simple

12. Jun 23, 2005

### HallsofIvy

No, for x close to -2, the denominator will be 2-|x|= 2-(-x)= 2+x. That's what you need. Now, what is the limit?

13. Jun 23, 2005

### naicidrac

Yes, thank you guys for all the help. Now I see that as you are close to -2, |x| is defined as -x so the problem looks something like this.

lim ((x+1)(x+2))/(2-|x|)
x->-2

since we said |x| is -x we get 2-(-x) which cancels with the numerator and we are left with (x+1) and after pluging in the limit we get the answer which is -1.

Thanks for all the help.