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Math Help - Limit Proof

  1. #1
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    Limit Proof

    Let g be defined on the Reals by g(1) = 0, and g(x) = 2 for all x not equal to 1. Let f(x) = x + 1 for all x in the Reals. Show that lim(as x->0) of g(f(x)) does not equal g(f(0)).

    I don't know how to go about proving this, so any help is much appreciated. Thanks!
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by jkru View Post
    Let g be defined on the Reals by g(1) = 0, and g(x) = 2 for all x not equal to 1. Let f(x) = x + 1 for all x in the Reals. Show that lim(as x->0) of g(f(x)) does not equal g(f(0)).

    I don't know how to go about proving this, so any help is much appreciated. Thanks!
    Simply notice that as x\to{0^\pm} you have that f(x)\to{1^{\pm}} so g(f(x))\to{2}\ne{g(f(0))=1}
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