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Math Help - uniformly convergent for function

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    uniformly convergent for function

    define function fn:[0,1]->R by fn(x)=(n^p)x*exp(-(n^q)x) where p , q>0 and
    fn->0 pointwise on[0,1] as n->infinite.,with the pointwise limit f(x)=0 ,and sup|fn(x)|=(n^(p-q))/e
    assume that ε is in (0,1)
    does fn converges uniformly on [1,1-ε]? how about on[0.1-ε]????

    my idea is checking whether the pointwise limit f is continuous on the interval above,but it is obvious,then f is continuous ,so fn is uniformly convergent,but i thought it is wrong. can someone give me any idea?????
    Last edited by cummings123321; November 5th 2012 at 03:39 PM.
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