Results 1 to 3 of 3

Math Help - Need Help With Limits

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    6

    Need Help With Limits

    This is a true/false question, and I have to say why it's true or false:

    lim (x,y)-->(0,0) |x^2 - y^2| / (x^2 + y^2) = 1


    just in case it's hard to interpret the question, it says that the limit as (x,y) approaches (0,0) of |x^2 - y^2| / (x^2 + y^2) is equal to 1.

    I'm not allowed to use L'Hospital's rule to explain this.
    Thanks in advance for your help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Oct 2009
    Posts
    6
    would it be enough to show that the function equals 0 along the line x=y and therefore prove the statement false?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Quote Originally Posted by magdaddy101 View Post
    This is a true/false question, and I have to say why it's true or false:

    lim (x,y)-->(0,0) |x^2 - y^2| / (x^2 + y^2) = 1


    just in case it's hard to interpret the question, it says that the limit as (x,y) approaches (0,0) of |x^2 - y^2| / (x^2 + y^2) is equal to 1.

    I'm not allowed to use L'Hospital's rule to explain this.
    Thanks in advance for your help.
    It's helpful to note that  |x^2 + y^2| = x^2 + y^2 for all real numbers. There will never be a time when  x^2 + y^2 is negative for any real numbers.

    Although I just realised that your expression is in fact  |x^2 - y^2 | so nevermind this!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Using limits to find other limits
    Posted in the Calculus Forum
    Replies: 7
    Last Post: September 18th 2009, 05:34 PM
  2. Function limits and sequence limits
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: April 26th 2009, 01:45 PM
  3. HELP on LIMITS
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 23rd 2008, 11:17 PM
  4. Limits
    Posted in the Calculus Forum
    Replies: 5
    Last Post: September 21st 2008, 10:52 PM
  5. [SOLVED] [SOLVED] Limits. LIMITS!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 25th 2008, 10:41 PM

Search Tags


/mathhelpforum @mathhelpforum