Answer Happy

(-1)-1 k=1 -uk 1. Recall that we derived the following Maclaurin Series in lecture, In(1+u) = Dyk which is valid when (ul< 1 on the interval of convergence I = (-1, 1). (a) (10 points) Find the Maclaurin series expansion of In(1 + 5 ) and determine its radius of convergence R. Use this to find the interval of convergence and draw a picture clearly indicating this interval. (b) (10 points) Use the Maclaurin series found in part (a) to determine the limit of lim In(1+ 22 (1+) 0

2. (a) (10 points) Find the equation of tangent line to the ellipse with parameters a and b at the point Xo = - 73a and yo = - using the parametric equations of the ellipse x = a cos(0) and y = b sin(). (b) (10 points) Find the exact value of the concavity at this point.