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Math Help - A "trivial" limit proof

  1. #1
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    A "trivial" limit proof

    I'm just clueless of how to prove this;

    Prove that lim f(x) = lim f(x-a)
    x->0 x->a

    I can see that making x to approach 0 is the same as making x approach a in (x-a), since both things go near zero. Well, I hope that you can help me
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  2. #2
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    Quote Originally Posted by akolman View Post
    I'm just clueless of how to prove this;

    Prove that lim f(x) = lim f(x-a)
    x->0 x->a

    I can see that making x to approach 0 is the same as making x approach a in (x-a), since both things go near zero. Well, I hope that you can help me
    Substitute u = x + a \Rightarrow x = u - a into \lim_{x \rightarrow 0} f(x):

    \lim_{u - a \rightarrow 0} f(u - a)

    \Rightarrow \lim_{u \rightarrow a} f(u - a).

    But u is just a dummy variable so you can re-brand it as x ......
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  3. #3
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    wow, that was fast!

    Thanks.
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