Need a little help please.

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:
111
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Is it x^2+3x+2 or x^2+3x-2?
 
22
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He must mean
[tex]\lim_{x\rightarrow -2}\frac{x^2+3x+2}{2-|x|}[/tex]
Otherwise it's undefined.
 
I edited my post and Vegeta was correct.
 

AKG

Science Advisor
Homework Helper
2,562
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As x approaches -2, x is negative.
 
2,209
1
Think of the absolute value funciton as a piecewise function, defined separately for positive numbers and negative numbers.
 
111
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Yes and keep in my to factor x^2+3x+2
 
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.
 
2,209
1
Defining piecewise functions is an algebraic method.
 
111
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As you approach -2 from left and right, lxl is defined as -x. Try to use this.
 
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
 

HallsofIvy

Science Advisor
41,626
821
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?
 
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.
 

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