Results 1 to 6 of 6

Math Help - Evaluting limit

  1. #1
    Member
    Joined
    Apr 2010
    Posts
    135

    Evaluting limit

    hello can some please show me how a question of this sort is evaluated.

    lim (tan x -sec x) as x tends to pi/2.

    thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2010
    From
    Clarksville, ARk
    Posts
    398

    Re: Evaluting limit

    First, realize that it's of the indeterminate form ∞ - ∞ .

    Express tan(x) and sec(x) in terms of sin(x) & cos(x) . Combine them into a single rational expression.

    See what you then have.

    Use L'H˘pital's rule if necessary.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member sbhatnagar's Avatar
    Joined
    Sep 2011
    From
    New Delhi, India
    Posts
    200
    Thanks
    17

    Re: Evaluting limit

    Correct!

    (1)Express the limit in the terms of sin(x) and cos(x).
    (2)Use L Hopital's rule.

    The correct answer is 0.

    To check click here.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Apr 2010
    Posts
    135

    Re: Evaluting limit

    Quote Originally Posted by SammyS View Post
    First, realize that it's of the indeterminate form ∞ - ∞ .

    Express tan(x) and sec(x) in terms of sin(x) & cos(x) . Combine them into a single rational expression.

    See what you then have.

    Use L'H˘pital's rule if necessary.
    Ok I have expressed it in terms of sin and cos.

    (Sinx-1)/cos x. Should I differenciate? Can you plz show me how to arrive at the answer from here. Thanks.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466

    Re: Evaluting limit

    sbhatnagar suggested you us L'Hopital's rule. Do you know what that is?

    If \lim_{x\to a} f(x)= 0 and \lim_{x\to a} g(x)= 0, then
    \lim_{x\to a}\frac{f(x)}{g(x)}= \lim_{x\to a}\frac{f'(x)}{g'(x)}

    Note that you differentiate the numerator and denominator separately, you do not differentiate the fraction.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,694
    Thanks
    450

    Re: Evaluting limit

    and if you can't use L'Hopital ...

    \lim_{x \to \frac{\pi}{2}} \tan{x} - \sec{x}

    \lim_{x \to \frac{\pi}{2}} \frac{\sin{x}-1}{\cos{x}}

    \lim_{x \to \frac{\pi}{2}} \frac{\sin{x}-1}{\cos{x}} \cdot \frac{\sin{x}+1}{\sin{x}+1}

    \lim_{x \to \frac{\pi}{2}} \frac{\sin^2{x}-1}{\cos{x}(\sin{x}+1)}

    \lim_{x \to \frac{\pi}{2}} \frac{-\cos^2{x}}{\cos{x}(\sin{x}+1)}

    \lim_{x \to \frac{\pi}{2}} \frac{-\cos{x}}{\sin{x}+1} = \frac{0}{2} = 0
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: September 20th 2010, 05:29 AM
  2. Replies: 1
    Last Post: August 8th 2010, 11:29 AM
  3. Replies: 16
    Last Post: November 15th 2009, 04:18 PM
  4. Limit, Limit Superior, and Limit Inferior of a function
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 3rd 2009, 05:05 PM
  5. Using the Central Limit Theorem to prove a limit
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: March 23rd 2009, 11:09 AM

Search Tags


/mathhelpforum @mathhelpforum