Results 1 to 2 of 2

Math Help - [SOLVED] The Squeeze Theorem

  1. #1
    Junior Member
    Joined
    Jul 2009
    Posts
    59

    [SOLVED] The Squeeze Theorem

    How do you solve this?

    \lim_{x\to\frac{\pi}{3}} (\sqrt{3} \sin x -2x)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by Mike9182 View Post
    How do you solve this?

    \lim_{x\to\frac{\pi}{3}} (\sqrt{3} \sin x -2x)
    Direct Substitution...

    That's all. There's no need for any advanced techniques here.

    I'll do it... Here's a step by step of all the relevant theorems of limits that apply.
    1. The limit of a sum is the sum of the limits.

    \lim_{x\to\frac{\pi}{3}}(\sqrt{3}\sin x-2x)=\lim_{x\to\frac{\pi}{3}}\sqrt{3}\sin{x}-\lim_{x\to\frac{\pi}{3}}2x

    2. The limit of a product is the product of the limits.

    =\lim_{x\to\frac{\pi}{3}}\sqrt{3}\cdot\lim_{x\to\f  rac{\pi}{3}}\sin{x}-\lim_{x\to\frac{\pi}{3}}2\cdot\lim_{x\to\frac{\pi}  {3}}x

    4. The limit of a constant is that constant

    =\sqrt{3}\lim_{x\to\frac{\pi}{3}}\sin{x}-2\lim_{x\to\frac{\pi}{3}}x

    5. The ovious limit

    =\sqrt{3}\lim_{x\to\frac{\pi}{3}}\sin{x}-2\frac{\pi}{3}

    6. The limit of transcendentals

    =\sqrt{3}\frac{\sqrt{3}}{2}-2\frac{\pi}{3}=\frac{3}{2}-\frac{2\pi}{3}

    You can see that there is no need for the squeeze theorem.
    Last edited by VonNemo19; August 7th 2009 at 08:09 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Squeeze Theorem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 8th 2010, 04:00 PM
  2. [SOLVED] squeeze theorem for sequences
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 11th 2010, 05:58 AM
  3. Squeeze theorem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 8th 2009, 07:43 PM
  4. Squeeze Theorem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 19th 2009, 11:21 PM
  5. [SOLVED] The Squeeze Theorem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 7th 2009, 08:09 AM

Search Tags


/mathhelpforum @mathhelpforum