1. Use Newton\'s method to approximate the value of x^3=45 as follows: let x1 =

ID: 2887186 • Letter: 1

Question

1. Use Newton's method to approximate the value of x^3=45 as follows:

let x1 = 3 be the initial approx.

find x2?

2.Use Newton's method to approximate a root of the equation 3sin(x) = x as follows: let x1 =2 be the inital approx.

The second approx. x2 is: ?

The third approx x3 is: ?

3. Use Newton's method to approximate a root of the equation 5x^7+8x^4+3=0 as follows: let x1 =1 be the initial approximation.

the second approximation x2 is:?

the third approximation x3 is:?

4. Use Newton's method to approximate a root of the equation e^-x=4+x correct to eight decimal places.

The root is:?

5. Use Newton's method to approximate a root of the equation cos(x^2+3) = x^3 as follows:

let x1 = 1 be initial approximation.

The second approximation x2 is:?

Use Newton's method to approximate the value of x^3=45 as follows:

let x1 = 3 be the initial approx.

find x2?

Soln :
f(x) = x^3 - 45
f'(x) = 3x^2

f(x1) = f(3) = -18
f'(x1) = f'(3) = 27

x2 = x1 - f(x1) / f'(x1)

x2 = 3 - (-18)/27

x2 = 3 + 2/3

x2 = 11/3 ---> ANS

---------------------------------------------------

2)
2.Use Newton's method to approximate a root of the equation 3sin(x) = x as follows: let x1 =2 be the inital approx.

The second approx. x2 is: ?

The third approx x3 is: ?

Soln :
f(x) = 3sinx - x
f'(x) = 3cosx - 1

x2 = x1 - f(x1)/f'(x1)

x2 = 2 - f(2)/f'(2)

x2 = 2 - (3sin(2) - 2)/(3cos(2) - 1) -->

x2 =2.323732 ---> ANS

x3 = x2 - f(x2)/f'(x2)

x3 = 2.323732 - f(2.323732)/f'(2.323732)

x3 = 2 - (3sin(2.323732) - 2).323732 / (3cos(2.323732) - 1))

x3 = 1.955862 ----> ANS

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.