Question

a. Find the linear approximating polynomial for the following function centered at the given point a. b. Find the quadratic approximating polynomial for the following function centered at the given point a. c. Use the polynomials obtained in parts a. and b. to approximate the given quantity. 1 Ca= 1; approximate 1.09 a. Py(x) = 0 b. P2(x)=0 1 1. c. Using the linear approximating polynomial to estimate, 16a is approximately (Type an integer or a decimal.) Using the quadratic approximating polynomial to estimate, 10 is approximately (Type an integer or a decimal.)

Answer 1

1.09 . +6) = ; a=1; La (a) line approximation PiC) = f(astt' cos(x-a) H() = * =1 ; I'VE GODF Picx) = 1-1(x-1) = 2-X Pi (X) = 2-x) ; $'(0) = -1 (6) Quedrale approximation 126) = f(a) + f(a)(x-a) + f"(a)(-aj? t°W) = a) = Dif"() = ? =2 {z (X) = 1 -1(xt) + ?(x-1)? P«) = (2-x +(-1,2 * Pi (1.09) = 2-1-09 = 10.91 P2 (1.09) = 2-1-09 +(1.09-1) =10.9181]