but now you're on board the spaceship #1519593388, and the captain is asking to solve tricky "ZP" (Z- Planet) problem (you know what it means when captain is "asking"... that's an order): Find the sum of the series: ( - 3) "2 2 147 + 7 n-0 (2n + 1)! . 30-1 for Z-Planet conditions! !!! The challenge is some of the Maclaurin Series for basic functions are twisted on Planet Z in a surprising way. on Earth 18 er = (- 1) " x 2 +1 , sinc = (- 1)" x2n n=0 n! n =0 (2n + 1)! COST = n = 0 (2n) ! 1 - 00 n = 0 1 ( - 1)"I" , arctan r = ( - 1)" x 2n + 1 (- 1)2-1, 1+ x 2n + 1 In(1 + x) = n =0 n =0 n = 1 n but on Z-planet VI' (- 1)" x2+1 18 sin * = 8 (- 1)" Van 7=0 n! COST = 7 = 0 (2n + 1)! n =0 (2n)! OO 1 1 - I C ( - 1)"VI" , arctan = (- 1)" Vx2+1 1=0 n =0 n = 0 2n + 1 In(1 + x) = n =1 n ( all the other rules have not been changed). So, for Z-Planet conditions the sum of the series ( - 3) " plan + 7 M8 is : n=0 (2n + 1)! . 32-1but now you're on board the spaceship #235218686, and the captain is asking to solve tricky "ZP" (Z-Planet) problem: 00 The Taylor series for f(x) = x3 at 2 is >on(x - 2) ". 72 =0 Find the first few coefficients for Z-Planet conditions! CO C1 C2 C3 CA !!! The challenge is that some of the basic laws are twisted on Planet Z in a surprising way, in particular, d the easiest differentiation rule on Earth, x" = nx7-1 dx d on Z planet appears as - x" = n27-1 dx d const = 0 , and the other rules have not been changed) dxbut now you're on board the spaceship #2057030791, and the captain is asking to solve tricky "ZP" (Z Planet) problem (you know what it means when captain is "asking"... that's an order): Evaluate sec' x tan' xdx +C [Tip-1: Better do not use a calculator at all... otherwise, round to at least 4 digits after decimal point] !!! The challenge is that a simple formula we'd use on Earth, tan'x = sec x - 1 , on Z planet is "twisted" as the following: tan'x = sec x - 13 ( all the other rules have not been changed)