Question

Use a calculator or program to compute the first 10 iterations of Newton's method for the given function and initial approximation. f(x)= 5 sinx- 4x-1, Xo = 1.9 Complete the table. (Do not round until the final answer. Then round to six decimal places as needed.) k хк XK 1 K 6 2 7 3 8 4 9 5 10

Answer 1

$\text{ Given }$

f(3) = 5sini 4.1 - 1

$\text{ Initial approximation, }x_0=1.9$

$\text{Calculating } f'(x)$

f'c) -(5sinu – 4.1 – 1) = 5cost – 4

$\text{ Using Newton's method }$

$x_k = x_{k-1}-\frac{f(x_k)}{f'(x_k)}$

$=> x_k = x_{k-1}-\frac{5sin(x_k)-4x_k-1}{5cos(x_k)-4}$

$\text{ Using this formula, we will compute first 10 iteration of Newton' method }$

	$x_k$		$x_k$
1	1.21122	6	-1.498735
2	0.691429	7	-1.49656
3	-3.202283	8	-1.496557
4	-1.855083	9	-1.496557
5	-1.555025	10	-1.496557