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Math Help - Limit Problem

  1. #1
    Senior Member topher0805's Avatar
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    Limit Problem

    \lim_{x \to 0} f(x)/x^2 = 6

    I'm supposed to find the limit of f(x) and the limit of f(x)/x. (As x approaches 0 in both cases)

    I've looked through the entire section of my textbook and I don't see anything directly covering this question. Any hints?
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  2. #2
    Flow Master
    mr fantastic's Avatar
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    Quote Originally Posted by topher0805 View Post
    \lim_{x \to 0} f(x)/x^2 = 6

    I'm supposed to find the limit of f(x) and the limit of f(x)/x. (As x approaches 0 in both cases)

    I've looked through the entire section of my textbook and I don't see anything directly covering this question. Any hints?
    I hope you can see that f(x) = 6x^2 satisfies \lim_{x \to 0} f(x)/x^2 = 6. So, without any further information, as far as I'm concerned that's a perfectly good rule for f(x).

    Then:

    \lim_{x \to 0} f(x) = \lim_{x \to 0} 6x^2 = 0.

    \lim_{x \to 0} \frac{f(x)}{x} = \lim_{x \to 0} \frac{6x^2}{x} = \lim_{x \to 0} 6x = 0.

    Personally, I think the question is pretty dumb.
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  3. #3
    Senior Member topher0805's Avatar
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    I agree, the question is dumb. When I first looked at it, my first inclination was to do what you did there, but it seemed like I was missing something. Thanks for the help.
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