## hawkfalcon Group Title Another lim problem, but different:( 2 years ago 2 years ago

1. hawkfalcon Group Title

$f(x) = \left[\begin{matrix}x^2-1 & x<1 \\ 4-x & x>=1\end{matrix}\right]$

2. hawkfalcon Group Title

I can do the lim, but how do i do it on that:O it lin x->1

3. hawkfalcon Group Title

$\lim_{x \rightarrow 1}$

4. Denebel Group Title

|dw:1346015959313:dw| Your graph will look something like this

5. Denebel Group Title

What is the limit for the function x^2 - 1 as it approaches 1?

6. hawkfalcon Group Title

Erm. -inf. right?

7. Denebel Group Title

Hmm, not quite. You want to approach x = 1.

8. Denebel Group Title

Follow the graph of x^2 -1 as it approaches x =1. What is the y-value?

9. hawkfalcon Group Title

0

10. hawkfalcon Group Title

I think:3

11. hawkfalcon Group Title

Sorry *.* i'm not very good a limits:(

12. Denebel Group Title

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.

13. Denebel Group Title

What would you say the limit was for that equation?

14. hawkfalcon Group Title

3

15. Denebel Group Title

Ok, are the two limits for both equations the same?

16. hawkfalcon Group Title

Nope. Oh:3. Dur dur. You compare the 2 equations:3

17. Denebel Group Title

18. hawkfalcon Group Title

DNE

19. hawkfalcon Group Title

@Denebel one last Q. It also says to find x->+ and -. In this cast, thats DNE too. right?

20. Denebel Group Title

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.

21. hawkfalcon Group Title

But those are not the same for either left or right.

22. Denebel Group Title

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

23. hawkfalcon Group Title

Oh so you only look at each problem separately then :O

24. hawkfalcon Group Title

so lim x->1- = 0 and + = 3 and x-> = DNE

25. Denebel Group Title

Yup.

26. hawkfalcon Group Title

<3 Thank you so much!