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Math Help - Help with simplifying Limits.

  1. #1
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    Question Help with simplifying Limits.

    For context: We have been working with the concept of limits in my Math 170 class. I understand what a Limit is quite well, but I am struggling with some of the algebra associated with finding limits. Here are two problems i'm having trouble with.

    1)The limit as x approaches -4 of (1/4 + 1/x) / (4+x)

    2)The limit as t approaches 0 of (sqrt(1+t) - sqrt(1-t)) / t


    These both seem to me to be simple, but when I try and simplify I seem to just work myself in circles, never able to reach a point in which I can use the limit law for quotients.

    Thanks for any help you may have.
    Last edited by mr fantastic; September 5th 2011 at 12:24 PM. Reason: Title.
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  2. #2
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    Re: Please help with simplifying Limits.

    Quote Originally Posted by iAmKrizzle View Post
    1)The limit as x approaches -4 of (1/4 + 1/x) / (4+x)

    2)The limit as t approaches 0 of (sqrt(1+t) - sqrt(1-t)) / t
    \frac{\frac{1}{4}+\frac{1}{x}}{4+x}=\frac{x+4}{4x(  x+4)}

    For #2 multiply by \frac{\sqrt{1+t}+\sqrt{1-t}}{\sqrt{1+t}+\sqrt{1-t}}
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