Question

Apply Newton's Method to approximate the x-value(s) of the indicated point(s) of intersection of the two graphs. Continue the iterations until two successive approximations differ by less than 0.001. [Hint: Let h(x) = f(x) − g(x).] f(x) = x4 g(x) = cos(x)

Answer 1

Answer:

n3 - n2 < 0.001

n3 - n2 = 2 * 10^-6

Step-by-step explanation:

For step by step solution check the two attachment

Answer 2

Answer:

-0.7548

Step-by-step explanation:

1. In this solution , I found out the approximation values of x by using the Newton's Method.

The initial value i.e x0=-1.

by using the x0 value find the next approximation x1 value.

Here two functions f(x) and g(x) are given.

we have to calculate h(x) = f(x) - g(x)

we know

Xn+1 = Xn - [ f(Xn) / f'(Xn) ]

by using above formula we will get the x1 value as

x1 = -0.83333

See the first attached image for the workings

2. we have to find the approximate values of x until their successive values differ by less than 0.001.

By following the above steps,we get

x2 = -0.7643988

x3 = -0.755026

x4 = -0.7548

the difference of x3 and x4 is i.e = 0.000148

Hence x value is = -0.7548

See the second attached image for the workings