Results 1 to 4 of 4

Math Help - Finding limit of this function, using Limit rules

  1. #1
    iva
    iva is offline
    Member iva's Avatar
    Joined
    Nov 2009
    From
    South Africa
    Posts
    81

    Finding limit of this function, using Limit rules

    I have some problems where I need to determine if the limits exist using the limit definition or limit laws. For the following 2 I think i can use the laws but would like to make sure:

    lim                <br />
](x,y)-> (0,0) = y/x^2

    I used the product rule splitting into 2 ie

    f(x,y) = y and g(x,y) = 1/x^2

    This would give a limit of 0 times infinity = 0 respectively right?


    Then the 2nd problem I thought I could handle the same way ie:

    lim                <br />
(x,y)-> (1,0)  y/x,

    I thought i could solve it the same way, ie use the product rule with 2 equations f(x,y)=y and g(x,y) = 1/x giving

    lim<br />
(x,y) -> (1,0) f(x,y) g(x,y) = (0)(1) = 0.

    I still need to do the proofs now but would like to know if i''m on the right track in terms of at least getting the limits right?

    many thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by iva View Post
    I have some problems where I need to determine if the limits exist using the limit definition or limit laws. For the following 2 I think i can use the laws but would like to make sure:

    lim <br />
](x,y)-> (0,0) = y/x^2


    Make y approach zero along the line y=x and then it follows

    at once that the limit doesn't exist.

    Tonio



    I used the product rule splitting into 2 ie

    f(x,y) = y and g(x,y) = 1/x^2

    This would give a limit of 0 times infinity = 0 respectively right?


    Then the 2nd problem I thought I could handle the same way ie:

    lim <br />
(x,y)-> (1,0) y/x,

    I thought i could solve it the same way, ie use the product rule with 2 equations f(x,y)=y and g(x,y) = 1/x giving

    lim<br />
(x,y) -> (1,0) f(x,y) g(x,y) = (0)(1) = 0.

    I still need to do the proofs now but would like to know if i''m on the right track in terms of at least getting the limits right?

    many thanks!
    .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    iva
    iva is offline
    Member iva's Avatar
    Joined
    Nov 2009
    From
    South Africa
    Posts
    81
    I'm sorry, I don't understand. For the line y=x, as y approaches zero the limit is tending to zero isn't it?
    Last edited by iva; February 27th 2011 at 04:50 AM. Reason: typo
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by iva View Post
    I'm sorry, I don't understand. For the line y=x, as y approaches zero the limit is tending to zero isn't it?

    \displaystyle{y=x\Longrightarrow \frac{y}{x^2}=\frac{x}{x^2}=\frac{1}{x}\xrightarro  w [x\to 0^+]{}\infty

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. finding limit of this function?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 26th 2010, 05:56 PM
  2. finding the limit of this function...
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 5th 2009, 07:11 PM
  3. Finding the limit of a triginometric function
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 29th 2009, 04:44 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. finding limit of a function
    Posted in the Calculus Forum
    Replies: 5
    Last Post: July 30th 2008, 11:46 PM

Search Tags


/mathhelpforum @mathhelpforum