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Math Help - Calculus II Homework Problem

  1. #1
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    Calculus II Homework Problem

    I ran across a problem in my Calculus II homework that I could use some help on.

    a)
    Consider the function f(x)=e^x
    Find the equation of a line p(x)=A+Bx with the property p(0)=f(0), and p ' (0)=f ' (0)
    Find p by setting up and solving these equations for A and B

    b)
    Next find the approximating quadratic, p2(x) = A + Bx + Cx2 such that,
    p2(0) = f(0); p2 ' (0) = f ' (0); and P2 " (0) = f " (0):
    by solving the equations for A, B, and C.

    c)
    Set up and find p4(x) explicitly for f(x)=e^x by extending the conditions as in the problems above

    d)
    Write your polynomials involving "n!". Discuss how you could guess p3 and p5, as well as why "n!" keeps showing up.

    Thank you for your help!
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by colonelone View Post
    I ran across a problem in my Calculus II homework that I could use some help on.

    a)
    Consider the function f(x)=e^x
    Find the equation of a line p(x)=A+Bx with the property p(0)=f(0), and p ' (0)=f ' (0)
    Find p by setting up and solving these equations for A and B

    Thank you for your help!
    p(0)=A+B*0 = A = f(0)
    p'(x)=B, so p'(0)=B=f'(0)

    And we know how to find f(0) and f'(0), right?
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  3. #3
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    Quote Originally Posted by chiph588@ View Post
    p(0)=A+B*0 = A = f(0)
    p'(x)=B, so p'(0)=B=f'(0)

    And we know how to find f(0) and f'(0), right?
    F(0) would just be e^0 or 1, and f'(0) would be e^0 or 1 as well. So A and B are each 1?
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  4. #4
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by colonelone View Post
    F(0) would just be e^0 or 1, and f'(0) would be e^0 or 1 as well. So A and B are each 1?
    correct.
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