Question

B.) Let R be the region between the curves y = x^3 , y = 0,...

B.) Let R be the region between the curves y = x^3 , y = 0, x = 1, x = 2. Use the method of cylindrical shells to compute the volume of the solid obtained by rotating R about the y-axis.

C.) The curve x(t) = sin (π t) y(t) = t^2 − t has two tangent lines at the point (0, 0). List both of them. Give your answer in the form y = mx + b ?

D.) For the following function, find the Taylor series representation centered at a = 1 and its radius of convergence f(x) = (2 + x)^5

E.) For the following function, find the Maclaurin series. f(x) = tan^(−1) (x/3)

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