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anonymous

  • one year ago

Find the indicated limit, if it exists. lim x->2 {x+3 x< 2 } {3-x x>_ 2}

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  1. anonymous
    • one year ago
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    Plug in \(x=2\) to both cases and see what happens.

  2. anonymous
    • one year ago
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    @wio you get 5 and 1.

  3. anonymous
    • one year ago
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    Do you know where I got \(2\) from?

  4. anonymous
    • one year ago
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    the limit as x approaches 2?

  5. anonymous
    • one year ago
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    Yes

  6. anonymous
    • one year ago
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    But there is another reason as well, both cases are split on 2.

  7. anonymous
    • one year ago
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    So we need to see if both cases approach 2 on both sides.

  8. anonymous
    • one year ago
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    The limit only exists if both sides approach the same number. You can graph it to see as well.

  9. anonymous
    • one year ago
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    how would you graph it?

  10. anonymous
    • one year ago
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    |dw:1434583292694:dw|

  11. anonymous
    • one year ago
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    so it DNE?

  12. anonymous
    • one year ago
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    @wio

  13. anonymous
    • one year ago
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    Yes

  14. anonymous
    • one year ago
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    Does it make sense how I graph it?

  15. anonymous
    • one year ago
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    Yea, can you help me with another one?

  16. anonymous
    • one year ago
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    lim x-> 0 {5x-9 x<0} { l 2-x l x>_0}

  17. anonymous
    • one year ago
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    |dw:1434583971277:dw|

  18. anonymous
    • one year ago
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    is that right? @wio

  19. anonymous
    • one year ago
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    Yes, that looks right

  20. anonymous
    • one year ago
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    do it DNE too?

  21. anonymous
    • one year ago
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    Yeah

  22. anonymous
    • one year ago
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    You don't have to graph it though, you can just plug in 0 and if both cases have a different value, then the limit doesn't exist.

  23. anonymous
    • one year ago
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    |dw:1434584238267:dw|

  24. anonymous
    • one year ago
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    lim x->5 { 5-x, x<5} { 8 , x=5} {x+3, x>5}

  25. anonymous
    • one year ago
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    is that right? @wio

  26. anonymous
    • one year ago
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    so it DNE right?

  27. anonymous
    • one year ago
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    It is DNE, though the graph isn't quite right

  28. anonymous
    • one year ago
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    8 and x+3 meet at x=5

  29. anonymous
    • one year ago
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    oh ok thank you so much!

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