Results 1 to 4 of 4

Math Help - limits and continuity

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    9
    Let F be a function defined by f(x)=2x-3 x≤4
    1+x x>4


    A. Find the limit of F(x) as x approaches 4 from the right


    B. Is F continuous on the interval from x=0 to x=10? why or why not


    Is there any way to do this without a graphing calc? if there is i cant figure it out.

    This didnt really come out the way i wanted F(x) is suppost to be defined by both of these 2x-3 x≤4 and 1+x x>4. i just cant type it like it is on the paper
    Last edited by mr fantastic; May 8th 2009 at 02:45 AM. Reason: Merged posts
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member mollymcf2009's Avatar
    Joined
    Jan 2009
    From
    Charleston, SC
    Posts
    490
    Awards
    1
    Quote Originally Posted by Yamahammer342 View Post
    Let F be a function defined by f(x)=2x-3 x≤4
    1+x x>4


    A. Find the limit of F(x) as x approaches 4 from the right


    B. Is F continuous on the interval from x=0 to x=10? why or why not


    Is there any way to do this without a graphing calc? if there is i cant figure it out.
    f(x) = { ^{2x-3}_{1+x} if ^{x \leq 4}_{x>4}

    A. \lim_{x \rightarrow 4^+} 1 + x = 5

    Because as x \rightarrow 4^+ concerns positive numbers greater than 4, you can use the 1+x part of the function to find the limit without having to graph it

    B. This is a piecewise function. Based on the conditions of the function, a piecewise function can be continuous or discontinuous depending on whether the stipulations given cause there to be a discontinuity. In the case of this piecewise function, it IS continuous on the interval (0,10) because there is no break in the graph. The two pieces of this function intersect at x=4. Should the function have read as:

    f(x) = { ^{2x-3}_{1+x} if ^{x<4}_{x>4}
    Then the function would not be continuous, because x = 2 would not be included in the domain of the function. There would be a hole at x=2
    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 mollymcf2009 View Post
    [snip]
    Should the function have read as:

    f(x) = { ^{2x-3}_{1+x} if ^{x<4}_{x>4}
    Then the function would not be continuous, because x = 2 would not be included in the domain of the function. There would be a hole at x=2
    Actually, the above function is continuous at x = 2. There's no hole at x = 2.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member mollymcf2009's Avatar
    Joined
    Jan 2009
    From
    Charleston, SC
    Posts
    490
    Awards
    1
    Quote Originally Posted by mr fantastic View Post
    Actually, the above function is continuous at x = 2. There's no hole at x = 2.
    I meant at 4, not 2. Sorry!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. limits and continuity
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 3rd 2010, 01:58 PM
  2. [SOLVED] Continuity with limits
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 17th 2010, 07:45 AM
  3. Limits and Continuity Help
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 19th 2009, 10:15 PM
  4. continuity and limits
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 28th 2008, 04:48 AM
  5. Limits and Continuity
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 3rd 2007, 07:31 PM

Search Tags


/mathhelpforum @mathhelpforum