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CSS Applied Mathematics QUESTION #4162
Question 1
Using Newton-Raphson method for $f(x) = \cos(x) - x = 0$ starting with $x_0 = \frac{\pi}{4}$, what is $x_1$?
  • $\frac{\pi}{4} - \frac{\cos(\pi/4) - \pi/4}{-\sin(\pi/4) - 1}$✔️
  • $\frac{\pi}{4} - \frac{\cos(\pi/4) - \pi/4}{-\sin(\pi/4)}$
  • $\frac{\pi}{4} + \frac{\cos(\pi/4) - \pi/4}{\sin(\pi/4) + 1}$
  • $\frac{\pi}{4} - \frac{\cos(\pi/4)}{\sin(\pi/4)}$
Correct Answer Explanation
Newton-Raphson: $x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$. Here $f'(x) = -\sin(x) - 1$. So $x_1 = x_0 - \frac{\cos(x_0) - x_0}{-\sin(x_0) - 1}$.