1. Use Newton\'s method with initial approximation x1 = 1 to find x2, the second
ID: 2860372 • Letter: 1
Question
1. Use Newton's method with initial approximation x1 = 1 to find x2, the second approximation to the root of the equation x4 x 2 = 0.
2. Use Newton's method to approximate the indicated root of the equation correct to six decimal places. The root of x^4 2x^3 + 7x^2 9 = 0 in the interval [1, 2]
3.Suppose the line y = 4x 1 is tangent to the curve y = f(x) when x = 2. If Newton's method is used to locate a root of the equation f(x) = 0 and the initial approximation is x1 = 2, find the second approximation x2.
4. Use Newton's method with the specified initial approximation x1 to find x3, the third approximation to the root of the given equation. (Give your answer to four decimal places.) x^5 + 8 = 0, x1 = 1
5. Use Newton's method to find all roots of the equation correct to six decimal places. (Enter your answers as a comma-separated list.) e^x = 9 3x
Explanation / Answer
1)
Given ,
f(x) = x^4 - x - 2
f ' (x) = 4x^3 - 1
Newton's method:
x_(n+1) = x_n - [f(x_n) / f ' (x_n)]
f(x_1) = f(1) = -2
f ' (x_1) = f ' (1) = 3
x_2 = x_1 - [f(x_1) / f ' (x_1)]
= 1 - (-2)/3 = 5/3 1.6667
which is the second approximate . it is not nearer to the true solution but repeated application of this law gives a true solution
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