Results 1 to 5 of 5

Math Help - Sandwich Theorem

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    73

    Sandwich Theorem

    Use the Sandwich/Squeeze Theorem to prove that

    \lim_{n\rightarrow  \infty} 2^{-n}\cos(n^3-n^2-13)

    exists.

    What is the limit?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by Caity View Post
    Use the Sandwich/Squeeze Theorem to prove that

    \lim_{n\rightarrow  infinity} 2^{-n}\cos(n^3-n^2-13)

    exists.

    What is the limit?
    |2^{-n} \cos (n^3 -n^2 -13) | \leq 2^{-n} \to 0
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,
    Quote Originally Posted by Caity View Post
    Use the Sandwich/Squeeze Theorem to prove that

    \lim_{n\rightarrow  infinity} 2^{-n}\cos(n^3-n^2-13)

    exists.

    What is the limit?
    Use the fact that -1 \leq \cos(x) \leq 1 \quad \text{for all x}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Sep 2008
    Posts
    73
    I did that Moo... then I got stuck... I have a problem saying it all... I was also wondering if I needed to use a subsequence to prove it...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Quote Originally Posted by Caity View Post
    I did that Moo... then I got stuck... I have a problem saying it all... I was also wondering if I needed to use a subsequence to prove it...
    Note that 2^{-n}=\frac{1}{2^n} \to 0

    -2^{-n} \leq 2^{-n} \cos(\dots)\leq 2^{-n}

    Finish it off
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: December 25th 2011, 06:54 PM
  2. Sandwich theorem generalization
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 4th 2009, 04:09 PM
  3. Sandwich Theorem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 9th 2009, 09:33 PM
  4. Sandwich Theorem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 9th 2009, 09:10 PM
  5. The Sandwich Theorem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 1st 2009, 03:56 PM

Search Tags


/mathhelpforum @mathhelpforum