Results 1 to 4 of 4

Math Help - Slant Asymptotes

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    8

    Slant Asymptotes

    Show that the curve y = square root (x^2 +4x) has two slant asymptotes y = x + 2 and y = x - 2.

    I am confused on where to start on this question, any help would be greatly appreciated, thanks so much in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,807
    Thanks
    116
    Quote Originally Posted by Amybee View Post
    Show that the curve y = square root (x^2 +4x) has two slant asymptotes y = x + 2 and y = x - 2.

    I am confused on where to start on this question, any help would be greatly appreciated, thanks so much in advance.
    1. The second asymptote should read: y = -x - 2

    2. The slope of the slant asymptote is calculated by:

    m = \lim_{ x \to \infty} \left(\dfrac yx \right) = \lim_{ x \to \infty} \left(\dfrac {\sqrt{x^2+4x}}x \right) = \lim_{ x \to \infty} \left(\dfrac {|x| \sqrt{1+ \frac4x}}x \right) = 1
    Or m = -1 which depends on the sign of x.

    Cab you take it from here?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    8
    I think so.
    Thanks for your help!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,807
    Thanks
    116
    Quote Originally Posted by Amybee View Post
    I think so.
    Thanks for your help!
    Nevertehless ... with your problem there exists a very elegant solution (and I have another opportunity to show off!):

    y=\sqrt{x^2+4x} = \sqrt{(x^2+4x+4)-4}=\sqrt{(x+2)^2-4}

    For very large values of x y is approaching

    a = \sqrt{(x+2)^2}=|x+2|

    ... and that's the equation of the asymptote.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Slant Asymptotes
    Posted in the Calculus Forum
    Replies: 5
    Last Post: September 5th 2010, 07:20 PM
  2. VA,HA & Slant Asymptotes
    Posted in the Algebra Forum
    Replies: 7
    Last Post: April 12th 2010, 06:31 PM
  3. slant asymptotes
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 28th 2009, 01:00 PM
  4. The vertical, horizontal, and slant asymptotes
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 13th 2008, 08:30 AM
  5. slant asymptotes
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 3rd 2008, 04:00 AM

Search Tags


/mathhelpforum @mathhelpforum