1) Taylor series

Find the first 4 NON ZERO terms of the Taylor series for f(x) at x=a is sigma[inf][n=0] (f^(n))(a)/(n!) * (x-a)^n

Find the first 4 NON ZERO terms of the Taylor series for cos(x) at x=pi/4

2) Write the Maclaurin series of the following functions. Determine the radius of convergence AND the interval of convergence (the boundary cases)

f(x) = x^3/(1+2x)^2

g(x) = integral ln(1-x^2)dx

3) Let f(x)=sin(2x)f(x)=\sin(2x)

f(x)=sin(2x). Find the smallest number of NON ZERO terms in the Maclaurin series, so that the value sin(2)\sin(2)

sin(2) is determined with precision 0.001. Hint: Make sure that you write the correct Maclaurin series