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Question 1: BOX answer please

Find the radius of convergence, R, of the series. 2 (5x 2)" n = 1 n5\" X Find the interval, 1', of convergence of the series. (Enter your answer using interval notation.) _ _l 1' 5'5 x Need Help? Find the radius of convergence, R, of the series. (x7 4}\" 5 ":0 n +1 J Find the interval of convergence, 1, of the series. (Enter your answer using interval notation.) I= (71,1) X Need Help? iii Find the area of the region that lies inside the first curve and outside the second curve. r = 1 + (205(6), r= 2 7 cos(9) H 4 x Need Help? , Submit Answer ' (a) Find a power series representation for f(x) = In(1 + x). f ( x ) = > n = 1 What is the radius of convergence, R? R = (b) Use part (a) to find a power series for f(x) = x In(1 + x). f ( x ) = > n = 2 What is the radius of convergence, R? R = (c) Use part (a) to find a power series for f(x) = In(x2 + 1). f(x) = > n = 1 What is the radius of convergence, R? R = Need Help? Read It(a) Use differentiation to find a power series representation for f (x) = (3 + x ) 2 00 f ( x ) = ( (-1)"(n+1) x" 3n+2 n = 0 What is the radius of convergence, R? R = 3 (b) Use part (a) to find a power series for f ( x ) = (3 + x ) 3 . 00 f ( x) = > ( ( -1)" ( n + 2) (n+1) *"+2 37+3 n = 0 X What is the radius of convergence, R? R = 3 (c) Use part (b) to find a power series for f ( x ) = (3 + x )3 00 f (x) = > ((-1)" (n +2)(n+1 ). x 7 + 2 on + 3 n = 2 X What is the radius of convergence, R? R = 3 Enhanced Feedback Please try again, keeping in mind that you can differentiate both sides of the power series expansion to obtain po series representation of the function a b+cx The resulting power series converges on the same interval