MAT136H1 Lecture 25: 10.2 Properties of Power Series
92
MAT136H1 Full Course Notes
Verified Note
92 documents
Document Summary
=1 y+y 2 y 3 +y 4 = ( )1 k 2k x n k=0. Set x=y 2 : ey2 = 1 + y2 + 2! y4 3! Set x= y 2 : ey2 = 1 y2 + 2! x6 3! x2 x2 = x2 x4 + 2! x8 + . e x5 + . inx s y6 + . y6 + . = x 3! x3 + 5! x. Suppose f(x)= ak e k = a0 + a1 c + a2 c 2 + . (x (x (x k=0 converges with radius r ak dx c k = d (x k=1 then. C k 1 = a 1 +2a 2 (x c)+3a 3 (x c) 2 + ak k(x f(x)= k=0 (t (t dt (t c)k+1 x ak k+1 x ak q (t c)2 + . k=0 q = (a0 c + a1 2.
