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 November 7th, 2008, 03:24 AM #1 Member   Joined: Jul 2008 Posts: 88 Thanks: 0 a Limit question. Hello friens. How it is proved : ? We cant's solve it by using Quotient Law, so How that is proved?! Thanks a lot.
 November 7th, 2008, 04:28 AM #2 Senior Member   Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3 Re: a Limit question. As x->a? Or as x->0 If x is anything but but 0, 1/x^2 is well-defined. Look at the definition of a limit. I'm taking this straight of of Stewart 5e: $\lim_{x\rightarrow a} f(x) = \infty \\ \text{ if for every positive number M, there exists a postive \delta such that\\ f(x) > M \text{ whenever } 0<|x-a|<\delta$ So, f(x) = 1/x^2, and a = 0. We want to be able to choose, for each M, a delta such that: $0< |x| < \delta \text{ means } \frac{1}{x^2} < M$ Can you find such a delta (relative to M)?
 November 7th, 2008, 01:26 PM #3 Senior Member   Joined: Jul 2008 Posts: 895 Thanks: 0 Re: a Limit question. Again, assuming 0 for "a", would not a study of fractions be sufficient? As the denominator decreases indefinitely, the value as a whole increases indefinitely.

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