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

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

Homework Statement



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

Homework Equations



N/A

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:

Answers and Replies

  • #2
97
0


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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