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Math Help - 2 Limit Questions

  1. #1
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    2 Limit Questions

    1) lim 1/x+4 - 1/4
    ------------
    x
    x->0

    This one i have no idea how to start it.....i'm totally lost...

    2) lim ------
    / t + 9 - 3
    ------------- that is suppose to be a square root sign over the t + 9
    t

    t->0

    For this question i got the answer of 1/6 but I dont know how to show my work using this.... forum but if someone can confirm 1/6 is the correct answer...also help me with number 1 thanks!
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  2. #2
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    Quote Originally Posted by justinwager View Post
    1) lim 1/x+4 - 1/4
    ------------
    x
    x->0

    This one i have no idea how to start it.....i'm totally lost...

    2) lim ------
    / t + 9 - 3
    ------------- that is suppose to be a square root sign over the t + 9
    t

    t->0

    For this question i got the answer of 1/6 but I dont know how to show my work using this.... forum but if someone can confirm 1/6 is the correct answer...also help me with number 1 thanks!
    In both cases you can use the theorem that f'(a) = \lim_{h \rightarrow 0} \frac{f(a + h) - f(a)}{h}.

    Otherwise you have to hack through the algebra the long way.

    Your answer to the second question is correct.
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  3. #3
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    Quote Originally Posted by justinwager View Post
    1) lim 1/x+4 - 1/4
    ------------
    x
    x->0

    This one i have no idea how to start it.....i'm totally lost...

    [snip]
    As an alternative to a calculus approach you should note that by getting a common denominator you have

    \frac{\frac{1}{x+4} - \frac{1}{4}}{x} = \frac{4 - (x + 4)}{4(x+4)x} = \, ....
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  4. #4
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    thanks for the help!

    based on your help i got

    -1/16 on the first question...is that correct?
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  5. #5
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    Quote Originally Posted by justinwager View Post
    thanks for the help!

    based on your help i got

    -1/16 on the first question...is that correct?
    Yes.
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