Answer:
This does not converge very well using an initial approximation of 1, but it does at 2.
Step-by-step explanation:
Newton's formula: formula:
xn+1=x − f(x)/f′(x)
You have x− 5sin(x)−x/5cos(x)−1
Use x=1 first off and then plug in the successive answers you get each time around.
1− 5sin(1)−1/5cos(1)−1 =−0.885
Now plug the -.885 in:
−.885− 5sin(−.885)−(−.885)/5cos(−.885)−1
−.885− 5sin(−.885)−(−.885)/5cos(−.885)−1=0.49264
You keep doing that until it converges to a solution.
It should converge to ±2.5957, but using an initial approximation of 1 it will not. Use 2 and it will.
Here is an animated graph showing what it does using x=1. The first graph is using x=2. See how it converges compared to the second one, which uses x=1?.
