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Math Help - Quick Limit Question

  1. #1
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    Quick Limit Question

    If there is a limit, for example:

    lim (x-->0) [(5-k)/x]

    where k is a constant and i needed to find values (if any) of k such that the limit exists.

    Would k=5 be the only value for k that would make the limit exist, and in this case the limit is equal to 0? Or does the limit still not exist?

    Thanks
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  2. #2
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    Quote Originally Posted by trivial123 View Post
    If there is a limit, for example:

    lim (x-->0) [(5-k)/x]

    where k is a constant and i needed to find values (if any) of k such that the limit exists.

    Would k=5 be the only value for k that would make the limit exist, and in this case the limit is equal to 0? Or does the limit still not exist?

    Thanks
    If k = 5 then the expression you're taking the limit of is the same 0. And it is trivial but true that \lim_{x \rightarrow 0} 0 = 0.
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  3. #3
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    Thanks for the reply, thought so. But is k=5 the only value of k for which the limit exists?
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  4. #4
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    Quote Originally Posted by trivial123 View Post
    Thanks for the reply, thought so. But is k=5 the only value of k for which the limit exists?
    If k is a constant, the numerator is going to be a constant for any value of k. The rational function y=\frac{a}{x}, where a is a constant, doesn't have a valid limit at 0.

    So yes to your question.
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