Results 1 to 4 of 4

Math Help - Another Trigo-limit

  1. #1
    Super Member dhiab's Avatar
    Joined
    May 2009
    From
    ALGERIA
    Posts
    534

    Another Trigo-limit

    Calculate this limit :
    <br />
\mathop {\lim }\limits_{x \to \frac{\pi }{2}} \left( {\sec x - \tan x} \right)<br />
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by dhiab View Post
    Calculate this limit :
    <br />
\mathop {\lim }\limits_{x \to \frac{\pi }{2}} \left( {\sec x - \tan x} \right)<br />
    There are numerous possible approaches including the use of l'Hopital's rule and power series. Please be clear on what approaches are NOT allowed.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member pacman's Avatar
    Joined
    Jul 2009
    Posts
    448


    sec x - tan x = (1/cos x) - (sin x)/(cos x) = (1 - sin x)/(cos x) =

    (1 - sin x)/(cos x), rationalize the numerator by its conjugate, (1 + sin x).

    = (1 - sin^2 x)/[(cos x)(1 + sin x],

    = (1 - sin^2 x)/[(cos x)(1 + sin x)],

    = (cos^2 x)/[(cos x)(1 + sin x)],

    = [cos x cos x]/[cos x (1 + sin x)],

    = ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,547
    Thanks
    539
    Hello, dhiab!

    Calculate this limit: . <br />
\lim_{x\to\frac{\pi}{2}}(\sec x - \tan x)

    Multiply by \frac{\sec x + \tan x}{\sec x + \tan x}

    . . \frac{\sec x - \tan x}{1}\cdot\frac{\sec x + \tan x}{\sec x + \tan x} \;=\;\frac{\overbrace{\sec^2\!x - \tan^2\!x}^{\text{This is 1}}}{\sec x + \tan x} \;=\;\frac{1}{\sec x + \tan x}


    Then: . \lim_{x\to\frac{\pi}{2}}\left(\frac{1}{\sec x + \tan x}\right) \;=\; \frac{1}{\sec\frac{\pi}{2} + \tan\frac{\pi}{2}} \;=\;\frac{1}{\infty + \infty} \;=\;0

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. limit-trigo
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 12th 2010, 08:40 PM
  2. Trigo-limit
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 30th 2010, 09:28 PM
  3. limit of trigo
    Posted in the Calculus Forum
    Replies: 6
    Last Post: November 9th 2009, 04:27 PM
  4. Trigo- limit( tan and sin)
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: August 9th 2009, 12:47 PM
  5. Trigo- limit
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: August 4th 2009, 11:59 PM

Search Tags


/mathhelpforum @mathhelpforum