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Math Help - Calculus Limit Question

  1. #1
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    Calculus Limit Question

    Hey guys, need help with a question

    "Give examples of two functions, f(x) and g(x), such that limx→1f(x) does not exist, limx→1g(x) does not exist, but limx→1(f(x)/g(x))=0."
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  2. #2
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    Quote Originally Posted by desperatestudent View Post
    Hey guys, need help with a question

    "Give examples of two functions, f(x) and g(x), such that limx→1f(x) does not exist, limx→1g(x) does not exist, but limx→1(f(x)/g(x))=0."
    1. a and b are real numbers with a\ne b\ \wedge\ a\ne 1\ \wedge\ b\ne 1.

    2. Let f(x)=\dfrac{x+a}{x-1} and g(x)=\dfrac{x+b}{(x-1)^2}. Then the limits

    \lim_{x \to 1}(f(x)) and \lim_{x \to 1}(g(x)) don't exist.

    3. You now can close the existing gap such that the limit \lim_{x \to 1}\left(\dfrac{f(x)}{g(x)} \right) = 0
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