Results 1 to 4 of 4

Math Help - limits

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    24

    limits

    let f be defined as follows where a is not equal to 0.
    f(x) = x^2-a^2 for x is not equal to a
    and f(x) = 0, for x=a

    which of the following are true about f?
    I. lim from x to a f(x) exists
    II. f(a) exists.
    III. f(x) is continuous at x=a

    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641

    Ok

    Quote Originally Posted by sandiego234 View Post
    let f be defined as follows where a is not equal to 0.
    f(x) = x^2-a^2 for x is not equal to a
    and f(x) = 0, for x=a

    which of the following are true about f?
    I. lim from x to a f(x) exists
    II. f(a) exists.
    III. f(x) is continuous at x=a

    I. and II. are correct...because we know the limit exists by how the question is worded...and we see that II. is correct becuase it states f(a)=0....and we see that three is incorrect because to have continuity at a point c f(c)=lim_{x \to c}f(x) which is not the case here
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Mathstud28 View Post
    [snip]we see that three is incorrect because to have continuity at a point c f(c)=lim_{x \to c}f(x) which is not the case here
    *Ahem* III is correct:

    \lim_{x \to a}f(x) = 0 = f(a) .....
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641

    Haha

    Quote Originally Posted by mr fantastic View Post
    *Ahem* III is correct:

    \lim_{x \to a}f(x) = 0 = f(a) .....
    Of course I would forget the problem and do something like that...haha thanks for catching my careless mistake
    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, 06:34 PM
  2. Function limits and sequence limits
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: April 26th 2009, 02:45 PM
  3. HELP on LIMITS
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 24th 2008, 12:17 AM
  4. Limits
    Posted in the Calculus Forum
    Replies: 5
    Last Post: September 21st 2008, 11:52 PM
  5. [SOLVED] [SOLVED] Limits. LIMITS!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 25th 2008, 11:41 PM

Search Tags


/mathhelpforum @mathhelpforum