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Math Help - Diffential Calculus...

  1. #1
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    Nov 2009
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    11

    Diffential Calculus...

    Hi
    Im not really sure how to do some questions....

    1. Find lim(x-> 0) [sin(6x+pi/6) - sin(pi/6)]/x, if it exists

    What I did was separate the numerator into sin(x) +sin(pi/6) - sin(pi/6). Since sin(pi/6) is equal to 1/2, they cancel out and it leaves to sin(x)/x, and this would = 1, not sure if I did it right or not...

    2. Given a thrice-differentiable function f(x), its Maclaurin polynomial of degree 3 is the polynomial of the form
    g(x) = a0 + a1x + a2x^2 + a3x^3
    (the 0, 1, 2, and 3, are subscript)
    satisfying the conditions g(0) = f(0), g'(0) = f'(0), g''(0) = f''(0) and g^(3) (0) = f^(3) (0). Find the Maclaurin polynomials of degree 3 for the following functions:
    a. f(x) = sinx
    b. f(x) = cosx
    c. f(x) = e^x

    Thanks alot for helping me guys..
    Last edited by mr fantastic; November 17th 2009 at 07:01 PM. Reason: Fixed an error in question
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