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Math Help - Limits at infinity

  1. #1
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    Limits at infinity

    1)The average cost/disc in dollars incurred by AA records in pressing x videodiscs is given by the average cost function

    C(x)=2.2+2500/x

    Evaluate lim x-->infinity C(x) and interpret your result

    2) true or false, if false why?...If limx-->a (x) exists, then f is defined at x=a
    I think this is true...what do you think?
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  2. #2
    Jen
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    Quote Originally Posted by lemontea View Post
    1)The average cost/disc in dollars incurred by AA records in pressing x videodiscs is given by the average cost function

    C(x)=2.2+2500/x

    Evaluate lim x-->infinity C(x) and interpret your result

    2) true or false, if false why?...If limx-->a (x) exists, then f is defined at x=a
    I think this is true...what do you think?
    \lim_{x \to \infty} (2.2+\frac{2500}{x})=2.2

    Consider for very very large values of x for example x=10^{99} if you tried to put this into a calculator you would get something like 2.5 \times 10^{-96}=.00000000000....25 with 95 zeros between the decimal and 25 which is essentially zero, and as x goes to infinity this would get closer and closer to zero.

    so all you would have left is 2.2

    Consider the graph of f(x)=\frac{x-1}{x^2-1}, shown below. Notice as x\to1, f(x) appears to approach 1/2. But the graph is not actually defined at that point.

    Limits at infinity-capture.jpg
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