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Math Help - Limits

  1. #1
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    Limits

    I have got a problem like this :

    Let f : R -> R be a function such that there exists constants b, m > 0 and c belongs to R such that
    f(x) > mx + c for all x > b

    using only the definition of the limit we have to prove that limit of f(x) when x goes to inifinity = inifinity

    I have tried to prove it like this :

    For all N > 0 if we can find some 'a' > 0 such that x > a implies (mx + c) > N
    then that in turn implies f(x) > N

    So that we can say limit of f(x) when x goes to inifinity = inifinity

    But the problem is I can't find an 'a' > 0 for this.

    I have tried to write it in reverse to find an 'a'

    i.e mx + c > N
    x > (N-c)/m

    But here I get stuck coz 'c' can be either >= N or <N

    So, can somebody please help me with this ?
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  2. #2
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    Re: Limits

    Quote Originally Posted by Kristen111111111111111111 View Post
    I have got a problem like this :
    Let f : R > R be a function such that there exists constants b, m > 0 and c belongs to R such that
    f(x) > mx + c for all x > b, using only the definition of the limit we have to prove that limit of f(x) when x goes to inifinity = inifinity
    Surely you realize that mx+c is a line with positive slope?

    So you know that {\lim _{x \to \infty }}\left( {mx + c} \right) = \infty now use simple comparison.
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