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
<em>See the first attached image for the workings</em>
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
<em>See the second attached image for the workings</em>
