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Math Help - Calculus

  1. #1
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    Calculus

    Let f: R-->R be a differentiable function such that f(0)=f(0)=0

    Demonstrate that if lim f(x)/f(x) exists, then that limit is equal to 0.
    x→0
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  2. #2
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    Re: Calculus

    I apologyze by not putting in an adequate form the limit when x tends to 0.
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  3. #3
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    Re: Calculus

    here take newton raphsons form of soln
    x(n+1)=x(n)-h(f(x(n))/f'(x(n)))
    now take limit on both sides

    lim(x(n+1)-x(n))=-hlim(f(x(n))/f'(x(n))) where x(n) -> 0

    as we see the lhs limit is equal to 0 so for rhs either h=0 or the limit is equal to 0

    but as we have taken h as some small value which is not equal to zero

    therefore we have our rhs limit as zero
    Thanks from Yeison
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