Results 1 to 8 of 8

Math Help - Maclaurin Series Help

  1. #1
    Len
    Len is offline
    Member
    Joined
    Mar 2008
    Posts
    93
    Thanks
    1

    Maclaurin Series Help

    Find the terms through x^6 in the Maclaurin series for f(x)

    f(x)=e^x sin(x)

    I'm not sure where to start this problem. I also have

    f(x)=\dfrac{1}{1+x+x^2}

    but perhaps with help to the first I will be able to solve the second. If you have time tho help/ hints would be appreciated. Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi

    Mac Laurin series of f is

    \sum^{+\infty}_{n=0} \frac{f^{(n)}(0)}{n!}\:x^n

    where f^{(n)} is the n-th derivative of f

    You have to calculate the derivatives of f up to the 6th one and use the formula
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Len
    Len is offline
    Member
    Joined
    Mar 2008
    Posts
    93
    Thanks
    1
    Quote Originally Posted by running-gag View Post
    Hi

    Mac Laurin series of f is

    \sum^{+\infty}_{n=0} \frac{f^{(n)}(0)}{n!}\:x^n

    where f^{(n)} is the n-th derivative of f

    You have to calculate the derivatives of f up to the 6th one and use the formula
    Could you or someone do the first derivative just so I can see how the formula is used?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    f(x)=e^x sin(x) is a product of 2 functions

    u(x)=e^x and v(x)=sin(x)

    You need to use the formula of derivation of a product : f'=u'v+uv'
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Len
    Len is offline
    Member
    Joined
    Mar 2008
    Posts
    93
    Thanks
    1
    Quote Originally Posted by running-gag View Post
    f(x)=e^x sin(x) is a product of 2 functions

    u(x)=e^x and v(x)=sin(x)

    You need to use the formula of derivation of a product : f'=u'v+uv'
    So

    f'(x)cosx e^x + sinx e^x

    So when I get the derivative what do I do?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Yes but it is better to factor

    f'(x)=e^x (\cos x + \sin x)

    You have to calculate all the derivatives up to the 6th one
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Len
    Len is offline
    Member
    Joined
    Mar 2008
    Posts
    93
    Thanks
    1
    Quote Originally Posted by running-gag View Post
    Yes but it is better to factor

    f'(x)=e^x (\cos x + \sin x)

    You have to calculate all the derivatives up to the 6th one
    I'm not sure I understand this and I appreciate your on-going help. The derivatives are as follows:

    f''(x)= 2cosx e^x
    f'''(x) = -2sinx e^x + 2cosx e^x
    f''''(x)=-4sinx e^x
    f'''''(x) = -4sinx e^x - 4cosx e^x
    f''''''(x)= -8cosx e^x

    What is the next step?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Quote Originally Posted by Len View Post
    I'm not sure I understand this and I appreciate your on-going help. The derivatives are as follows:

    f''(x)= 2cosx e^x
    f'''(x) = -2sinx e^x + 2cosx e^x
    f''''(x)=-4sinx e^x
    f'''''(x) = -4sinx e^x - 4cosx e^x
    f''''''(x)= -8cosx e^x
    OK

    The next step is to apply the formula

    \sum^{+\infty}_{n=0} \frac{f^{(n)}(0)}{n!}\:x^n

    where f^{(n)} is the n-th derivative of f

    You are asked only the terms up to x^6

    \sum^{6}_{n=0} \frac{f^{(n)}(0)}{n!}\:x^n
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: January 26th 2010, 08:06 AM
  2. Replies: 2
    Last Post: September 16th 2009, 07:56 AM
  3. Binomial Series to find a Maclaurin Series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 21st 2009, 07:15 AM
  4. Multiplying power series - Maclaurin series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 7th 2009, 11:24 PM
  5. Replies: 1
    Last Post: May 5th 2008, 09:44 PM

Search Tags


/mathhelpforum @mathhelpforum