PLEASE HELP WITH THSES CALCULUS QUESTIONS. SHOW ALL WORK!!!

D Find a power series representation for the function and determine the interval of convergence f ( X = XI *4 + 15 () Evaluate the indefinite integral as a pacer Series . what is the radius of convergence 7 - 8 by tan dx (B) use the definition of a Taylor series to find the first four non zero terms of the series for fox ) centered at the given value of a f ( x ) = sin x a = u/6 use a Maclaurin series in Table , to obtain the maclaurin Series for |the given functions ) . Refer to the image below ab foxE X COS (LAZY ( b) f ( x ) = xi l n ( + + x 3 ) 12 number a (5) Approximate f by a Taylor polynomial with degree n at the f ( x ) = x P, a = p n = 3 0 . 8 * * 41 2Table 1 Important Maclaurin Series 1 >x" -Itxtxtx' +.. and Their Radii of - x n=0 R = 1 Convergence 73 X X ex = = 1 + + n=0 n! 1! 2! 3! R = 00 2n+1 X' sin x = >(-1)" + (2n + 1)! 3! 5! 7! n=0 R = co x 2n 4 r COs x = >(-1)" = + (2n)! 2! 4! 6! R = 0O n=0 00 -2n+1 7 tan x = >(-1)" =X - -+ n=0 2n + 1 3 5 7 R =1 -n In ( 1 + x) = >(-1)7-12 X r = X + n 2 3 4 R = 1 1=1 (1 + x)* = > k k(k - 1) k(k - 1)(k - 2) (x" = 1 + kx+ x + x3+ .. R= 1 1= 2! 3