Basic Calculus Help: Solving a Limit Problem with Algebra

  • Thread starter naicidrac
  • Start date
In summary, Vegeta was correct; as x approaches -2, x is negative and the absolute value function is a piecewise function that is defined separately for positive and negative numbers.
  • #1
naicidrac
14
0
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:
Physics news on Phys.org
  • #2
Is it x^2+3x+2 or x^2+3x-2?
 
  • #3
He must mean
[tex]\lim_{x\rightarrow -2}\frac{x^2+3x+2}{2-|x|}[/tex]
Otherwise it's undefined.
 
  • #4
I edited my post and Vegeta was correct.
 
  • #5
As x approaches -2, x is negative.
 
  • #6
Think of the absolute value funciton as a piecewise function, defined separately for positive numbers and negative numbers.
 
  • #7
Yes and keep in my to factor x^2+3x+2
 
  • #8
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
Defining piecewise functions is an algebraic method.
 
  • #10
As you approach -2 from left and right, lxl is defined as -x. Try to use this.
 
  • #11
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
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
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.
 

1. What does "Need a little help please." mean?

"Need a little help please." is a request for assistance or support in a particular matter.

2. Who typically says "Need a little help please."?

Anyone who needs help can say "Need a little help please." This phrase is commonly used when someone is struggling with a task or problem and requires assistance.

3. Why do people say "Need a little help please."?

People say "Need a little help please." because they are unable to complete a task or solve a problem on their own and require assistance from others.

4. How can I respond to someone who says "Need a little help please."?

You can respond to someone who says "Need a little help please." by offering your assistance and asking them specifically what they need help with. You can also provide words of encouragement and support.

5. Is it appropriate to say "Need a little help please." in a professional setting?

Yes, it is appropriate to say "Need a little help please." in a professional setting. Asking for help when needed shows humility and a willingness to learn and improve, which are valuable traits in a professional setting.

Similar threads

  • Introductory Physics Homework Help
Replies
28
Views
259
  • Introductory Physics Homework Help
Replies
24
Views
890
  • Introductory Physics Homework Help
Replies
5
Views
841
  • Introductory Physics Homework Help
Replies
3
Views
669
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
198
  • Introductory Physics Homework Help
Replies
17
Views
363
  • Introductory Physics Homework Help
Replies
4
Views
209
  • Introductory Physics Homework Help
Replies
3
Views
191
  • General Math
Replies
22
Views
397
Back
Top