Find the Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4, and then find the nth Maclaurin polynomials for the function in sigma notation.

1)sinh x

2)xe^x

3)ln(1+x)

4)cos PIx

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- Nov 3rd 2008, 08:45 PMnoles2188Maclaurin polynomials
Find the Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4, and then find the nth Maclaurin polynomials for the function in sigma notation.

1)sinh x

2)xe^x

3)ln(1+x)

4)cos PIx - Nov 3rd 2008, 08:51 PMbadgerigar
The formula for the nth Maclaurin polynomial is $\displaystyle f(x) \approx \sum_{k=0}^n\frac{1}{k!}f^{(k)}(0)x^k$ where $\displaystyle f^{(k)}(0)$ is the kth derivative of f at x=0.