maths

1- find the convergence interval for: sigma from n=1 to infinity ( x-1)^n/n^4 +10

2- find the Maclaurin series for f(x)= sinx

3- consider the solid obtained by rotating the region bounded by the given line y=2
y=2x, y=2 square root of x
find the volume V of this solid


4- find the length for r=4cos theta, theta bigger than or equal to 0, and smaller than or equal to pi/4


5- consider the solid obtained by rotating the region bounded by the given curves about the x-axis,
y=x^3, y=x, x bigger than or equal to 0
find the volume v of this solid.


6- find the length of the curve y=( x^2/6)/(1/2x) with x bigger than or equal to 1/2 , and smaller than or equal to 2.
( instruction: leave your answer in a single fraction without converting it into decimals).