Find the Taylorseries centered atx=0 for the following function: f(x)=6^x . Answer: Sum (infinity at top, n=0 at bottom) (Be sure to indicate all multiplications explicitly with an asterisk)

Find the Taylorseries centered atx=4 for the following function: f(x)=e^x Answer: Sum (infinity at top, n=0 at bottom) (Be sure to indicate all multiplications explicitly with an asterisk)

The Taylorseries forsin(x) centered atx=0is given by:Sum (infinity at top, n=0 at bottom) (((-1)^n)(x^2n+1))/(2n+1)! . Using this result, determine a power series representation forf(x)= (x^4)(sin(x^2)). Answer: Sum (infinity at top, n=0 at bottom) (Be sure to indicate all multiplications explicitly with an asterisk)