Use Newton's method to obtain an approximation to the root of $\cos ^{-1} x-6 x=0$ to within 0.00001.
A) 0.20844
B) 0.2443
C) 0.22413
D) 0.2712

Question

Quizplus · Accepted Answer

Newton's method is used to find successively better approximations to the roots (or zeroes) of a real-valued function. For the function $f(x) = \cos^{-1} x - 6x$, applying Newton's method with an initial guess and iterating will converge to the root approximately at 0.22413.

Use Newton's Method to Obtain an Approximation to the Root cos⁡−1x−6x=0\cos ^{-1} x-6 x=0cos−1x−6x=0

Use Newton's Method to Obtain an Approximation to the Root $\cos ^{-1} x-6 x=0$