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hawkfalcon

  • 3 years ago

Another lim problem, but different:(

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  1. hawkfalcon
    • 3 years ago
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    \[f(x) = \left[\begin{matrix}x^2-1 & x<1 \\ 4-x & x>=1\end{matrix}\right]\]

  2. hawkfalcon
    • 3 years ago
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    I can do the lim, but how do i do it on that:O it lin x->1

  3. hawkfalcon
    • 3 years ago
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    \[\lim_{x \rightarrow 1}\]

  4. Denebel
    • 3 years ago
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    |dw:1346015959313:dw| Your graph will look something like this

  5. Denebel
    • 3 years ago
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    What is the limit for the function x^2 - 1 as it approaches 1?

  6. hawkfalcon
    • 3 years ago
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    Erm. -inf. right?

  7. Denebel
    • 3 years ago
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    Hmm, not quite. You want to approach x = 1.

  8. Denebel
    • 3 years ago
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    Follow the graph of x^2 -1 as it approaches x =1. What is the y-value?

  9. hawkfalcon
    • 3 years ago
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    0

  10. hawkfalcon
    • 3 years ago
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    I think:3

  11. hawkfalcon
    • 3 years ago
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    Sorry *.* i'm not very good a limits:(

  12. Denebel
    • 3 years ago
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    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
    • 3 years ago
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    What would you say the limit was for that equation?

  14. hawkfalcon
    • 3 years ago
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    3

  15. Denebel
    • 3 years ago
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    Ok, are the two limits for both equations the same?

  16. hawkfalcon
    • 3 years ago
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    Nope. Oh:3. Dur dur. You compare the 2 equations:3

  17. Denebel
    • 3 years ago
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    What is your final answer for the problem?

  18. hawkfalcon
    • 3 years ago
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    DNE

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

  20. Denebel
    • 3 years ago
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    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
    • 3 years ago
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    But those are not the same for either left or right.

  22. Denebel
    • 3 years ago
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    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
    • 3 years ago
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    Oh so you only look at each problem separately then :O

  24. hawkfalcon
    • 3 years ago
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    so lim x->1- = 0 and + = 3 and x-> = DNE

  25. Denebel
    • 3 years ago
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    Yup.

  26. hawkfalcon
    • 3 years ago
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    <3 Thank you so much!

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