Results 1 to 3 of 3

Math Help - limit and graph

  1. #1
    Member
    Joined
    Sep 2005
    Posts
    136

    limit and graph

    1>
    Let f(x)=|x-1|+x-1
    (a) sketch the graph of f(x)
    (b) find lim x-> -2f(x)
    (c) find lim x->2 f(x)

    2> Find a cutoff distance δ such that if the distance from x to 1 is less than δ and x>1, then f(x) =3x-1. approximates 2 with an error of at most 1/100
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by bobby77 View Post
    1>
    Let f(x)=|x-1|+x-1
    (a) sketch the graph of f(x)
    (b) find lim x-> -2f(x)
    (c) find lim x->2 f(x)
    The curve is below.
    Note if your graphing software does not have the absolute value function you can graph y=sqrt(x^2) that is a nice trick to replace it.

    To find the limits is very easy.
    Note that,
    f1=|x| is continous everywhere,
    f2=x-1 is continous everywhere,
    Thus,
    f1 o f2=|x-1| is continous everywhere, (by composition rule).
    Thus,
    (f1 o f2)+f2=|x-1|+x-1 is continus everywhere, (by addition rule of continous functions).
    Thus,
    to find the limits of f=|x-1|+x-1
    All we need to is evaluate the function at those points.
    Attached Thumbnails Attached Thumbnails limit and graph-picture1.gif  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by bobby77 View Post

    2> Find a cutoff distance δ such that if the distance from x to 1 is less than δ and x>1, then f(x) =3x-1. approximates 2 with an error of at most 1/100
    Put x=1+x. x>0.

    Then f(x)=2+3u, and if the error here is <=1/100 ,we have

    f(x)-2<=1/100,

    or:

    3u<=1/100,

    u<=1/300

    So if 0<(x-1)<δ,and 0<=δ<=1/300 then f(x) =3x-1. approximates 2 with an error
    of at most 1/100.

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding limit of discontinous function (graph)
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 31st 2010, 01:51 AM
  2. finding one sided limit[no graph]
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 4th 2010, 06:14 AM
  3. Specific Point of Limit on graph
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 5th 2009, 01:32 PM
  4. Replies: 1
    Last Post: September 8th 2008, 05:31 AM
  5. Limit graph with decimals
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 12th 2007, 12:51 PM

Search Tags


/mathhelpforum @mathhelpforum