Results 1 to 4 of 4

Math Help - [SOLVED] Taylor inequality to estimate accuracy of approximation

  1. #1
    Senior Member mollymcf2009's Avatar
    Joined
    Jan 2009
    From
    Charleston, SC
    Posts
    490
    Awards
    1

    [SOLVED] Taylor inequality to estimate accuracy of approximation

    f(x) = sec(x) \rightarrow a=0, n=2, -0.3 \leq x \leq 0.3

    Here is my Taylor polynomial approximation:

    T_2(x) = 1 + \frac{1}{2}x^2

    So, then I found my (n+1) derivative:

    f^3(x) = secxtanx(tan^2x + 5sec^2x)

    So,
    <br />
\left|R_n\right| \leq \frac{M}{(n+1)!} \left|x-a\right|^{n+1}

    CAn someone show me how to do this part?
    I know that I need to find a suitable M. How do I do that with these trig fuctions? Can I just choose zero for my x, since it is within my interval?

    Thanks!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    no--- a is 0

    Rn depends on x -- the max value of x on your interval is .3 So if you're trying to find an upper bound for the error for all x in the interval use .3

    To find M I'd do it graphically making sure to use |f^3(x)| on your graph
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member mollymcf2009's Avatar
    Joined
    Jan 2009
    From
    Charleston, SC
    Posts
    490
    Awards
    1
    Quote Originally Posted by Calculus26 View Post
    no--- a is 0

    Rn depends on x -- the max value of x on your interval is .3 So if you're trying to find an upper bound for the error for all x in the interval use .3

    To find M I'd do it graphically making sure to use |f^3(x)| on your graph

    Right, forgot that my a was = 0. Thanks!
    The instructions say to find M and then check my answer by graphing. So to find M, do I just plug in .3 into my third derivative and solve? Is that what I use for my M???
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    Generally no

    but since sec(x) and tan(x) are increasing 0n (0,.3)

    and from symmetry concerns |sec(x)tan(x)| is the same on (-.3,.3)

    you can just use f^3 (.3) for M in this case
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: May 15th 2011, 07:38 PM
  2. linear approximation accuracy question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 14th 2010, 04:08 PM
  3. Replies: 1
    Last Post: March 9th 2010, 04:56 AM
  4. Replies: 1
    Last Post: November 30th 2009, 02:25 PM
  5. [SOLVED] Taylor Polynomial approximation
    Posted in the Calculus Forum
    Replies: 8
    Last Post: June 13th 2009, 08:39 PM

Search Tags


/mathhelpforum @mathhelpforum