Chapter 10.2, Problem 18E

Fill in the coefficients of the degree 3 Taylor polynomial for f(x) = sin x centered at x = 3 T3(x) = [ Select ] %D [ Select ] - (x – ) + [ Select ] (x - 5)² 3 [ Select ] - (x - 5)* IT 3

Find the Taylor polynomial of order 3 generated by f at a

Exercise 5: Let f and g be functions with sixth-order Taylor polynomials (about 0): P6.f(x= 1-+2x2 -53 +x4 - 6, Pe.g(x) = x - x2+x3 -2x4 x6. Compute the following sixth-order Taylor polynomials (a) (f g) (x), about x = 0 (b) (fg)(x), about x = 0 (c) fog(x), about x = 0 Explain why you do not have enough information to compute the sixth-order Taylor polynomial for go f(x) about x = 0.