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Homework Help: Prove that cos:R->[-1,1] is continuous at every a∈R

  1. Mar 15, 2010 #1
    Prove that cos:R-->[-1,1] is continuous at every a∈R

    1. The problem statement, all variables and given/known data

    Prove that cos:R-->[-1,1] is continuous at every a∈R

    2. Relevant equations

    N/A

    3. The attempt at a solution

    If the function is right continuous at -1, and left continuous at 1, then should the function be continuous in the interval? so the limit of cos(x) as it approaches -1 from the right towards -1 should be the same as cos(-1), and vice versa for the other side. Please confirm or deny this.

    Thanks in advance,
    Charismaztex
     
    Last edited: Mar 15, 2010
  2. jcsd
  3. Mar 15, 2010 #2
    Re: Prove that cos:R-->[-1,1] is continuous at every a∈R

    I think you may have your domain and your range confused: you need to show that cos is continuous at every point in [tex]\mathbb{R}[/tex], not just in the interval: [-1,1].

    I suggest using a delta/epsilon argument...
     
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