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Math Help - Limits

  1. #1
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    Limits

    Im struggling with this problem. lim h approaching 0 f(x+h)-f(x)/h for f(x)=4x^2-x
    if anyone could help me that would be great
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  2. #2
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    Quote Originally Posted by mxhockey140 View Post
    Im struggling with this problem. lim h approaching 0 f(x+h)-f(x)/h for f(x)=4x^2-x
    if anyone could help me that would be great
     f(x) = 4x^2-x

     f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}

     = \lim_{h \to 0} \frac{4(x+h)^2-(x+h) - 4x^2+x}{h}

     = \lim_{h \to 0} \frac{4x^2+8xh+4h^2-x-h - 4x^2+x}{h}

     = \lim_{h \to 0} \frac{8xh+4h^2-h}{h}

    Take out a factor of h on the top and bottom, and you should get a result you can work with.

     = \lim_{h \to 0} 8x+4h-1
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  3. #3
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    thank you!
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