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Thread: Please help me on this problem?

  1. #1
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    Question Please help me on this problem?

    The equation for this problem is would be 3 + (1/(x-4)^2)

    This is the problem:

    The limit of r(x) as x approaches infinity is 3. How large would you have to keep x in order for r(x) to be within 0.01 unit of 3? How large would you have to keep x in order for r(x) to be within epsilon units of 3 where epsilon is a small positive number.

    Please can someone help me solve it step by step.
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by Plasma540 View Post
    The equation for this problem is would be 3 + (1/(x-4)^2)

    This is the problem:

    The limit of r(x) as x approaches infinity is 3. How large would you have to keep x in order for r(x) to be within 0.01 unit of 3? How large would you have to keep x in order for r(x) to be within epsilon units of 3 where epsilon is a small positive number.

    Please can someone help me solve it step by step.
    You want $\displaystyle \left(3+\frac{1}{(x-4)^2}\right)-3<\epsilon$. So,

    $\displaystyle \left(3+\frac{1}{(x-4)^2}\right)-3=\frac{1}{(x-4)^2}<\epsilon \implies (x-4)^2>\frac{1}{\epsilon}$ $\displaystyle \implies x-4>\sqrt{\frac{1}{\epsilon}}\implies x>4+\sqrt{\frac{1}{\epsilon}}$.

    For the first part, let $\displaystyle \epsilon=0.01$ and solve for $\displaystyle x$. You should get $\displaystyle x>14$.
    Last edited by redsoxfan325; Oct 21st 2009 at 05:00 PM.
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