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Math Help - Continuity of 1/x

  1. #1
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    Continuity of 1/x

    Show that 1/x is continuous on at any c =/= 0
    hint: chose delta to stay away from 0

    i have a general idea of how it works but I'm not really sure how to
    "use delta = min{[c]/2,c^2(e/2)} "(answer from book)
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by mtlchris View Post
    Show that 1/x is continuous on at any c =/= 0
    hint: chose delta to stay away from 0

    i have a general idea of how it works but I'm not really sure how to
    "use delta = min{[c]/2,c^2(e/2)} "(answer from book)
    Did you try writing out the definition?

    \left|\frac{1}{x}-\frac{1}{c}\right|=\left|\frac{c-x}{xc}\right|....how look that the \delta. It's \min because obviously we want to restrict our attention so that we may apply some estimation (i.e. on "whatever" neighborhood of c it is always true that "whatever" is less than or equal to "whatever else"). Also, use that in conjunction with the fact that you really only care about bounding \frac{1}{|xc|} for one can make |c-x| as arbitrarily small as one wants.
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