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Math Help - Stuck on Limit Problem

  1. #1
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    Stuck on Limit Problem

    Hi, I don't know how to approach this...I'm stuck ... I tried using the conjugate to find the limit and solved for x, but it still doesn't work... it always give me zero (unless I did it wrong). Can you show me how to solve this?

    <br /> <br />
\lim_{x \to 4} \frac{x^3-64}{x-4}<br /> <br /> <br />
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  2. #2
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    If you plug four in, you get 0/0, so you need to apply L'Hopital's Rule and take the derivative of the numerator and the derivative of the denominator (separately, not using the quotient rule). This gives you the limit as x approaches 4 of 3 x^2 or 48.

    Edit: Hope that helped! Also, what did you use to get the expression as a nice little picture with all the symbols? I'm new to this.
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  3. #3
    Super Member General's Avatar
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    Quote Originally Posted by kdl00 View Post
    Hi, I don't know how to approach this...I'm stuck ... I tried using the conjugate to find the limit and solved for x, but it still doesn't work... it always give me zero (unless I did it wrong). Can you show me how to solve this?

    <br /> <br />
\lim_{x \to 4} \frac{x^3-64}{x-4}<br /> <br /> <br />
    x^3-64=(x-4)(x^2+4x+16).
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  4. #4
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by kdl00 View Post
    Hi, I don't know how to approach this...I'm stuck ... I tried using the conjugate to find the limit and solved for x, but it still doesn't work... it always give me zero (unless I did it wrong). Can you show me how to solve this?

    <br /> <br />
\lim_{x \to 4} \frac{x^3-64}{x-4}<br /> <br /> <br />

    Reduce <br /> <br />
\lim_{x \to 4} \frac{x^3-64}{x-4}<br /> <br /> <br />
    to

    (x-4)(x^2+4x+16) / (x-4)

    and evaluate the expression (x^2+4x+16) as limit tends to 4
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  5. #5
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    That way works too! Another method would be long division if you can't remember the formula for those darned cubics.
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  6. #6
    Super Member General's Avatar
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    Well, there is another method.
    take f(x)=x^3 then f(4)=64.
    By the limit definition of the derivative:

    \lim_{x\to 4} \frac{x^3-64}{x-4}=f'(4)=3(4)^2=48
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  7. #7
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    Quote Originally Posted by General View Post
    x^3-64=(x-4)(x^2+4x+16).
    lol that was simpler then i thought... thank you!
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