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Homework Help: Prove this statement (limits and sequences)

  1. Feb 21, 2015 #1
    1. The problem statement, all variables and given/known data
    Let lim f(x)=a as x appr. infinity
    Let xn be a sequence so that lim xn=infinity as n appr. infinity. Prove using definitions that then lim f(xn)=a as n appr. infinity.

    2. Relevant equations

    3. The attempt at a solution
    I have had hard time trying to grasp how to begin with this...

    Because lim f(x)=a as x appr. infinity there
    Last edited: Feb 21, 2015
  2. jcsd
  3. Feb 21, 2015 #2


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    2017 Award

    Staff: Mentor

    And that is good otherwise the statement would be wrong.

    I would try to use the elementary definitions of convergence for the function and the sequence.
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