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anonymous

  • one year ago

Use the given graph to determine the limit, if it exists. -2; 6 1; 1 Does not exist; does not exist 6; -2

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    find

  3. freckles
    • one year ago
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    Do you know how to evaluate f(2.1)?

  4. freckles
    • one year ago
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    from looking at the graph

  5. anonymous
    • one year ago
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    nope @freckles

  6. ganeshie8
    • one year ago
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    |dw:1438030387764:dw|

  7. anonymous
    • one year ago
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    @ganeshie8 help

  8. ganeshie8
    • one year ago
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    Imagine you're walking on the graph, towards x=2, from the right side : |dw:1438030518779:dw|

  9. anonymous
    • one year ago
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    ok so what do i do next? @ganeshie8

  10. ganeshie8
    • one year ago
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    what value does the graph takes as you approach x=2 ?

  11. anonymous
    • one year ago
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    idk 2? @ganeshie8

  12. ganeshie8
    • one year ago
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    careful, values down that horizontal axis are negative so i think you mean -2 ?

  13. anonymous
    • one year ago
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    yes. so is that the final answer? -2? @

  14. ganeshie8
    • one year ago
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    |dw:1438030838624:dw|

  15. ganeshie8
    • one year ago
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    Yes, so we say the limit from right hand side of x=2 is \(-2\) and we write it mathematically as : \[\Large \lim\limits_{x\to2^{+}}~~f(x)~~~=-2\]

  16. ganeshie8
    • one year ago
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    see if you can guess the limit from left hand side : \[\Large \lim\limits_{x\to2^{\color{red}{-}}}~~f(x)~~~= ?\]

  17. anonymous
    • one year ago
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    would it be 6? @ganeshie8

  18. ganeshie8
    • one year ago
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    Perfect! You do knw these things!

  19. anonymous
    • one year ago
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    so the answer is -2;6 @ganeshie8

  20. freckles
    • one year ago
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    And if you notice f is approaching -2 if you plug in values to the right of x=2 like f(2.5)=-2 f(2.3)=-2 f(2.1)=-2 These numbers don't all usually appear the same but these numbers are approaching -2 as x approaches x=2 you can do the same thing for the left... also I know f(2.1)=-2 from just looking at: |dw:1438031090291:dw|

  21. freckles
    • one year ago
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    and also I probably could have drawn 2.1 closer to 2 but it is kind of hard to draw it closer to 2.1 without making it ugly and not readable

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