Assignment

This week study was on Taylor series, please attempt all the provided question and attach all relevant documents. Late submission will not be accepted and the assignment must be in student own work thus the assignment MUST be in document form.

1. Determine a Taylor Series about x=0x=0 for the following integral.cos(x)1xdxcos(x)1xdx
2. Write down T2(x)T2(x), T4(x)T4(x) and T6(x)T6(x) for the Taylor Series of f(x)=sin(x)f(x)=sin(x) about x=32x=32. Graph all three of the Taylor polynomials and f(x)f(x) on the same graph for the interval [,2][,2].
3. Write down T2(x)T2(x), T3(x)T3(x) and T4(x)T4(x) for the Taylor Series of f(x)=ln(1x)f(x)=ln(1x) about x=2x=2. Graph all three of the Taylor polynomials and f(x)f(x) on the same graph for the interval [4,0][4,0].
4. write down T1(x)T1(x), T3(x)T3(x) and T5(x)T5(x) for the Taylor Series of f(x)=1(6x)7f(x)=1(6x)7 about x=4x=4. Graph all three of the Taylor polynomials and f(x)f(x) on the same graph for the interval [1,5][1,5].
5. Write down T2(x)T2(x), T4(x)T4(x) and T6(x)T6(x) for the Taylor Series of f(x)=2+xf(x)=2+x about x=1x=1. Graph all three of the Taylor polynomials and f(x)f(x) on the same graph for the interval [2,4][2,4].