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Math Help - limit of 2^x - 32 / x-5

  1. #1
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    Exclamation limit of 2^x - 32 / x-5

    i can't figure it out for some reason it's weird!

    each limit represents the derivative of some function "f" at some number "a". state such an "f" and "a" in each case.

    limit as x-->5

    2^x - 32 / x-5

    i keep trying but i can't get it right!

    if it helps i know the answer in the back of the book says
    f(x)=2^x, a=5

    please and thank you!
    Last edited by mr fantastic; September 27th 2009 at 03:19 AM.
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  2. #2
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    Quote Originally Posted by jayjay60 View Post
    i can't figure it out for some reason it's weird!

    each limit represents the derivative of some function "f" at some number "a". state such an "f" and "a" in each case.

    limit as x-->5

    2^x - 32 / x-5

    i keep trying but i can't get it right!!!!
    if it helps i know the answer in the back of the book says
    f(x)=2^x, a=5

    please and thank you!
    are you familiar with the difference quotient?

    f'(a) = \lim_{x \to a} \frac{f(x) - f(a)}{x-a}

    match it up ...

    f'(5) = \lim_{x \to 5} \frac{f(x) - f(5)}{x-5}

    f'(5) = \lim_{x \to 5} \frac{2^x - 2^5}{x-5}
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  3. #3
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    Smile

    yes, well i can't understand how f(x)=2^x, a=5 is the answer though? :<
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  4. #4
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    Talking

    oh gosh. i hate when they're so simple it's easy to overlook!!! thank you so much.
    Last edited by mr fantastic; September 27th 2009 at 03:20 AM.
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