buestions 19 and 20 refer to expansion of functions in power series and involve concepts like uniqueness of the Taylor (or Maclaurin) series; termwise integration; and termwise differentiation. 19....

buestions 19 and 20 refer to expansion of functions in power series and involve concepts like uniqueness of the Taylor (or Maclaurin) series; termwise integration; and termwise differentiation.
19. (Select the choice which gives complete correct information.)
Suppose f(x) = a0 + ak(x - c)k, convergent in some interval k=1 lx - cl

fk(c) a) ak b) The series may have been developed by any means; whatever the method, it would not matter. c) With c * 0, series is the (only) Taylor series for f(x). d) With c 0, series is the (only) Maclaurin series for f(x). e) All of the above a). b). c). and d) are true.
20. (Select Suppose a) b) Jx c) the choice which gives complete correct information.) f(x) a0 + a1x + a2x2 + akxk k=0 co f'(x) a1 + 2a2x + 3a3x2 + kakxk-1 k-1 co a2 3 f(t) dt a0x +r1 x2 + -rx + e 0 k=0 Ix' < r="" co="" a="" xk="" is="" ills="" maclaurin="" series="" for="" fix)="" k="k" t=""> co a k k+1 is Maclaurin for for Ixi

d) None of a), b), nor c) is true. e) All three of a), b), and c) are true.