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Math Help - limit help

  1. #1
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    limit help

    if limx->a[f(x) + g(x)] = 2, and limx->a[f(x) - g(x)] = 1, find limx->a[f(x)g(x)]


    please explain how the answer is 3/4!!!!
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  2. #2
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    Re: limit help

    \lim_{x \to a} \left[f(x)+g(x)]^2 = 2^2

    \lim_{x \to a} \left[f(x)^2 + 2f(x)g(x)+g(x)^2] = 4

    \lim_{x \to a} \left[f(x)-g(x)]^2 = 1^2

    \lim_{x \to a} \left[f(x)^2 - 2f(x)g(x)+g(x)^2] = 1


    \lim_{x \to a} \left[f(x)^2 + 2f(x)g(x)+g(x)^2] -\lim_{x \to a} \left[f(x)^2 - 2f(x)g(x)+g(x)^2] = 4 - 1

    \lim_{x \to a} \left[f(x)^2 + 2f(x)g(x)+g(x)^2] - \left[f(x)^2 - 2f(x)g(x)+g(x)^2] = 3

    \lim_{x \to a} 4f(x)g(x) = 3

    4 \lim_{x \to a} f(x)g(x) = 3

    \lim_{x \to a} f(x)g(x) = \frac{3}{4}
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