Question

x=tanx by Newtown Rephson method​

Answer 1

We need to use an iterative method to solve this problem, and I choose to use Newton-Raphson for this equation which can also be written as x=tan(x).

Clearly the roots of tan(x)−x are given by the intersections of y=x and y=tan(x). So the first 3 roots are around 3π/2, 5π/2, and 7π/2.

Here is my iteration scheme so far with x0=3π/2:

xn+1=xn−f(xn)f′(xn)=xn−xn−tan(xn)1−1cos2(xn)

Answer 2

Answer:

Explanation:  We need to use an iterative method to solve this problem, and I choose to use Newton-Raphson for this equation which can also be written as x=tan(x).

Clearly the roots of tan(x)−x are given by the intersections of y=x and y=tan(x). So the first 3 roots are around 3π/2, 5π/2, and 7π/2.

Here is my iteration scheme so far with x0=3π/2:

xn+1=xn−f(xn)f′(xn)=xn−xn−tan(xn)1−1cos2(xn)