Find the third term of the Taylor polynomial for f(x) = cosx, centered at x = 1/2.?

Question

a. 1/3! (x-pi/2)^3
b. 1/3! (x^3)
c.-1/5! (x-pi/2)^5
d.-(x-pi/2)^5
e. none of these

Answer 1

y=cos x
y´=-sin x
y´´=-cos x
y´´´=sinx
cosx = cos(1/2)-sin1/2 *(x-1/2) -cos(1/2) (x-1/2)/2!+sin1/2 *(x-1/2)^3/3!
I suppose that you meant x= pi/2
In this case the third term is (x-pi/2)^3/3! (a)

Answer 2

A circle has a formula equation: (x-h)^2 + (y-ok)^2 = r^2 (x+a million)^2 + (y+3)^2 = 9/4 to locate radius (r) set r^2 = 9/4 So, r =sqrt(9/4) = 3/2 the middle is the element (h,ok) on your equation h = -a million and ok = -3 So the middle is (-a million,-3)