Find the Maclaurin series for the givon function and the interval of convergence

Question

Find the Maclaurin series for the givon function and the interval of convergence f(x) = 2e2x g(x) = ln(1 - x2) Find a power series solution of the form to the differential equation y'' = y with initial condition y(0) = 1 y(0) -1 Find the volume of the solid obtained by rotating the region enclosed by y = x2 - 1 and y = 2x - 1 about the axis y = 4 Sketch the region bounded by y = and y = 1 for x [0,4] and find its centroid Calculate the surface area of the solid obtained by rotating y = 2/3x3/4 - 2/5x5/4 about the x-axis on the interval [0, Use Simpson's Rule to approximate sin(x2)dx with n = 8 partitions, (i.e. find S8).

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