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Math Help - Products of limits

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    Products of limits

    Can you give an example to show why infinity times zero should not be defined?
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  2. #2
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    Quote Originally Posted by Slazenger3 View Post
    Can you give an example to show why infinity times zero should not be defined?
    \lim_{x\to 0} ax= 0 for all x and \lim_{x\to 0}\frac{1}{x}= \infty but \lim_{x\to 0}(ax)(\frac{1}{x})=\lim_{x\to 0}a= a. If we defined " 0(\infty)" to be any specific value, the rule \lim_{x\to a} f(x)g(x)= \left(\lim_{x\to a}f(x)\right)\left(\lim_{x\to a} g(x)\right) would not be true since the above examples would be of the form " 0(\infty)" but the limit of the product depends upon a.
    Last edited by HallsofIvy; February 6th 2010 at 04:45 AM. Reason: LaTeX fix
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