A 1 B 124 C 14 D 14 What is the coefficient of x 14 in the

A. 1

B. -1/24

C. 1/4

D. -1/4

What is the coefficient of (x - 1)4 in the fourth-degree polynomial approximation of f(x) = In x about x = 1?

Solution

If f(x) = ln x,
f\'(x) = 1/x
f\'\'(x) = -1/x²
f\'\'\'(x) = 2/x³
f\'\'\'\'(x) = -6/x⁴

Then, the coefficient of the fourth degree term at 1 is f\'\'\'\'(x)/4! =  -6/1⁴ /4! = -6/24 = -1/4

D.