Use Newton's Method to find the solution of the equation x + tan x = 0 on the interval [2, 3] accurate to four decimal places.
A) 2.0288
B) 2.0293
C) 2.0278
D) 2.0272
E) 2.0284

Question

Quizplus · Accepted Answer

Newton's Method formula is $x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$, where $f(x) = x + \tan(x)$. The derivative, $f'(x) = 1 + \sec^2(x)$. Starting with an initial guess $x_0$ in the interval [2, 3], we iteratively apply the formula until the change in $x$ is less than the desired accuracy, which is four decimal places in this case. After performing the iterations, the value that converges to the solution of $x + \tan(x) = 0$ within the given interval and accuracy is approximately 2.0288.

Use Newton's Method to Find the Solution of the Equation