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Math Help - 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 \left(3+\frac{1}{(x-4)^2}\right)-3<\epsilon. So,

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

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