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Math Help - continuity

  1. #1
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    Lightbulb continuity

    Hi I'm posting an image which discusses a problem and a possible incorrect argument.

    Would like to why the argument posted in the problem is incorrect, if it is.
    continuity-continuity2.jpg
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  2. #2
    Super Member girdav's Avatar
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    Re: continuity

    Can you detail 1-\delta <1-xC<1+\delta C\Rightarrow |1-xC|<1+\delta C?
    Hint: if f were continuous at x=0, then for \varepsilon=1 we would find a \delta>0 such that if |x-0|<\delta then |f(x)-f(0)|\leq 1. Notice that for n large enough, \frac 1n<\delta.
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