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Math Help - Limits

  1. #1
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    Limits

    Use the Divergence Criterion for Functional Limits corollary:
    (Let f be a function defined on A, and let c be a limit point of A. If there exist two sequences (x_n) and (y_n) in A with x_n \not= c and y_n \not= c and lim x_n=lim y_n= c but lim f(x_n) \not=lim f(y_n), then we conclude that the functional limit lim_{x\rightarrow c} f(x) does not exist.)the
    to show that the following limit does not exist.

    lim_{x\rightarrow 0} |x|/x

    Thanks!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by shadow_2145 View Post
    Use the Divergence Criterion for Functional Limits corollary:
    (Let f be a function defined on A, and let c be a limit point of A. If there exist two sequences (x_n) and (y_n) in A with x_n \not= c and y_n \not= c and lim x_n=lim y_n= c but lim f(x_n) \not=lim f(y_n), then we conclude that the functional limit lim_{x\rightarrow c} f(x) does not exist.)the
    to show that the following limit does not exist.

    lim_{x\rightarrow 0} |x|/x

    Thanks!
    take f(x) = \frac {|x|}{x}, c = 0, x_n = \frac 1n and y_n = - \frac 1n
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