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Math Help - Limits w/ Lhopitals Urgent help:

  1. #1
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    Limits w/ Lhopitals Urgent help:


    Evaluate the lim
    1.) No matter how I use Lhopital its always undefined because of the e
    answer at the book for this is 0

    2.) Helpp... this ones hard too...
    Thanks ahead...
    Last edited by ^_^Engineer_Adam^_^; March 11th 2007 at 09:00 AM.
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  2. #2
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    Talking Re:

    Hi Engineer_Adam!

    When situations such as these arrive. I mean ones you plug in the variable and the solution yields undefined; it's always a good habit to calculate the left and right hand limits by setting up a table. If a solution is said to be undefined it is because the the numbers at a certain point on the graph are heading in two totally different directions. You can see the work for problem one by clicking the link under #1. Keep in mind you can solve any limit problem by looking at a graph or setting up a table.

    1.

    http://item.slide.com/r/1/209/i/JXOn...E2Gsyds0QYUB_/

    2.

    I am still working on this problem. I know the answer is 0 because when you take the limit of both the left and right and side the number is limiting 0. I will keep you posted when I get the work.

    Best of Luck!
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  3. #3
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    Hello, ^_^Engineer_Adam^_^!

    I think I've got the first one . . .



    . . . . . e^{-1/x}
    . lim . -----------
    x→0+ . . . x

    . . . . . . . . . . . . . . . . . . . . x^{-1} . . . . .
    Rewrite the function: . lim . ---------- . . ---
    . . . . . . . . . . . . . . . x→0+ .e^{1/x} . . . .

    . . . . . . . . . . . . . . . . . . .-x^{-2} . . . . . . . . . . . . .1
    Apply L'Hopital: . lim . -------------------- . = . lim . ---------- . = . 0
    . . . . . . . . . . . .x→0+ -x^{-2}e^{1/x} . . .x→0+ e^{1/x}

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