Results 1 to 4 of 4

Math Help - graphing a sequence

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    5

    Question graphing a sequence

    Hi guys, i have a problem with this past homework question i've come accross whilst studying for my exams:


    Sketch the graphs of
    f(x) = (1 + x)^(1/2) and g(x) = x on the same axes. Let the sequence

    a
    n
    be defined by a0 = 0 and an+1 = &1 + an for any n # 0. Interpret the sequence an

    graphically using your sketch.


    Here is the solution:


    Starting at
    (an, an) on the graph of g and moving vertically to the the graph of f we reach the point

    (
    an, an+1). Moving horizontally back to the graph of g takes us to (an+1, an+1). This is represented

    by the dotted zig-zag line.

    graphing a sequence-solution-graphing-sequence.jpg

    I don't understand how this is the solution, am i plotting a graph of a against a n+1? any help would be much appreciated, thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Here's a start, \displaystyle (0,0),(0,1),(1,1),(1,f(1)),\dots = (0,g(0)),(g(0),f(0)),(f(0),g(f(0))),\dots
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2010
    Posts
    5
    i just don't understand the relationship between the sequence and the coordinates, if i didn't know the solution, i would just plot a0, a1, a2 etc. on the x axis and plot the corresponding value.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jan 2010
    Posts
    5
    Right I think I understand this now so I'll leave how I understood it here for any other newbie members. The question asks to plot a sequence on the graph, we already have the function f(x) which defines the sequence, we just have to find the x-coordinates along the graph of f(x) which defines each term of the sequence. Because this is a sequence, each x-coordinate is the previous y/ f(x) coordinate. So to find this point we use the function g(x) which for any y-coordinate will an equal x-coordinate. Hence the zig zag is used to find a(n) along f(x). If anyone can see a mistake with this please explain.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: August 24th 2010, 02:10 AM
  2. Replies: 0
    Last Post: July 4th 2010, 12:05 PM
  3. Replies: 2
    Last Post: March 1st 2010, 11:57 AM
  4. sequence membership and sequence builder operators
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: June 4th 2009, 03:16 AM
  5. Replies: 12
    Last Post: November 15th 2006, 12:51 PM

Search Tags


/mathhelpforum @mathhelpforum