hawkfalcon
  • hawkfalcon
Another lim problem, but different:(
Mathematics
katieb
  • katieb
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hawkfalcon
  • hawkfalcon
\[f(x) = \left[\begin{matrix}x^2-1 & x<1 \\ 4-x & x>=1\end{matrix}\right]\]
hawkfalcon
  • hawkfalcon
I can do the lim, but how do i do it on that:O it lin x->1
hawkfalcon
  • hawkfalcon
\[\lim_{x \rightarrow 1}\]

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anonymous
  • anonymous
|dw:1346015959313:dw| Your graph will look something like this
anonymous
  • anonymous
What is the limit for the function x^2 - 1 as it approaches 1?
hawkfalcon
  • hawkfalcon
Erm. -inf. right?
anonymous
  • anonymous
Hmm, not quite. You want to approach x = 1.
anonymous
  • anonymous
Follow the graph of x^2 -1 as it approaches x =1. What is the y-value?
hawkfalcon
  • hawkfalcon
0
hawkfalcon
  • hawkfalcon
I think:3
hawkfalcon
  • hawkfalcon
Sorry *.* i'm not very good a limits:(
anonymous
  • anonymous
Yes :) then follow the graph of 4-x as it approaches x=1. You start from the right hand side and move back till you reach x=1.
anonymous
  • anonymous
What would you say the limit was for that equation?
hawkfalcon
  • hawkfalcon
3
anonymous
  • anonymous
Ok, are the two limits for both equations the same?
hawkfalcon
  • hawkfalcon
Nope. Oh:3. Dur dur. You compare the 2 equations:3
anonymous
  • anonymous
What is your final answer for the problem?
hawkfalcon
  • hawkfalcon
DNE
hawkfalcon
  • hawkfalcon
@Denebel one last Q. It also says to find x->+ and -. In this cast, thats DNE too. right?
anonymous
  • anonymous
Nope, as x->+ means when x approaches a number (in this case, 1) from the right hand side. x->- means when x approaches (1) from the left hand side.
hawkfalcon
  • hawkfalcon
But those are not the same for either left or right.
anonymous
  • anonymous
You only need to make sure they are the same when they don't give you a +/- Since the next part of the problem asks you to state the limit when it comes from +, then when it comes from - you say what you told me before. So when x-> 1+ is when it approaches x=1 from the right side. You only look at the function 4-x in this case. x-> 1- is when it approaches x=1 from the left side, so look at the function x^2 - 1
hawkfalcon
  • hawkfalcon
Oh so you only look at each problem separately then :O
hawkfalcon
  • hawkfalcon
so lim x->1- = 0 and + = 3 and x-> = DNE
anonymous
  • anonymous
Yup.
hawkfalcon
  • hawkfalcon
<3 Thank you so much!

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