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Math Help - One sided limit proof

  1. #1
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    One sided limit proof

    Let s,t ele R and f1,f2 : (s,t) -> R. Take a ele (s,t) and suppose lim x->a- f1(x) and lim x-> a- f2(x) exist and equal L1 and L2 respectively.

    Suppose L1=-inf and L2=inf. Then , does the limit L = lim x->a- f1(x) + f2(x) exist? Explain your idea briefly.

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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by tbyou87 View Post
    Let s,t ele R and f1,f2 : (s,t) -> R. Take a ele (s,t) and suppose lim x->a- f1(x) and lim x-> a- f2(x) exist and equal L1 and L2 respectively.

    Suppose L1=-inf and L2=inf. Then , does the limit L = lim x->a- f1(x) + f2(x) exist? Explain your idea briefly.

    Thanks
    it depends. we can have almost anything happen here. if f_1 = f_2, then the limit is zero, which exists. if f_1 greatly overwhelms f_2, then the limit goes to the limit of f_1 and vice versa.
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