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The Newton-Raphson algorithm is used to approximate the zero of f(x) = x^3 + x - 5 between x = 1 and x = 2

Question : The Newton-Raphson algorithm is used to approximate the zero of f(x) = x^3 + x - 5 between x = 1 and x = 2 : 2163550

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the Newton-Raphson algorithm to approximate the given root to the nearest thousandth.

1) √(2)

A) 1.419

B) 2.000

C) 1.411

D) 1.414

2) (3)√(4)

A) 1.578

B) 1.593

C) 1.583

D) 1.587

Use the Newton-Raphson algorithm to find a zero of the function on the given interval. Round your answer to the nearest hundredth.

3) f(x) = 4x2 + 14x - 13; between 0 and 1

A) 0.76

B) 0.77

C) 0.78

D) 0.75

4) f(x) = ex + 6x - 6; between 0 and 1

A) 0.67

B) 0.64

C) 0.65

D) 0.66

5) The Newton-Raphson algorithm is used to approximate the zero of f(x) = x3 + x - 5 between x = 1 and x = 2. If x0 = 1, find x1.

A) (7/3)

B) (7/4)

C) (1/4)

D) (3/4)

E) none of these

6) The Newton-Raphson algorithm is applied to estimate √(10). If x0 = 3, find x2.

A) (700/237)

B) (5/3)

C) (721/228)

D) (758/521)

E) none of these

7) The Newton-Raphson algorithm is applied to estimate a zero of f(x) with x0 = 3. Which of the following statements is true?

A) x1 = 3 - (f'(3)/f(3))

B) x1 = 3 - (f(3)/f'(3))

C) x1 = 3 + (f'(3)/f(3))

D) x1 = (f'(3)/f(3))

E) none of these

8) Below is a graph of the function f(x). If x0 is taken as the initial approximation of the zero of f(x), then which of the following points, A, B, C, or D could be given by the Newton-Raphson algorithm as the next approximation?

A) A

B) B

C) C

D) D

9) Below is a graph of the functions h(x) and g(x). In using the Newton-Raphson algorithm to find where h(x) = g(x), which of the following statements is false?

A) Use the Newton-Raphson algorithm to find the zeroes of f(x) = g(x) - h(x).

B) Use the Newton-Raphson algorithm to find the zeroes of f(x) = h(x) - g(x).

C) x0 = 3 could be used as the initial approximation.

D) x0 = 4 could be used as the initial approximation.

E) Use the Newton-Raphson algorithm to find the zeroes of f(x) = h(x) + g(x).

10) Suppose x0 is an initial approximation of a zero of the function f(x). Using the Newton-Raphson algorithm, a second approximation, x1 is obtained. Which of the following must be true?

A) x1 = x0 - (f'(x0) /f(x0))

B) f(x1) = 0

C) x1 is the x-coordinate of the x-intercept of the tangent line to f(x) at (x0, f(x0))

D) x1 is closer to the zero of f(x) than x0 .

E) all of these

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

11) Let x0= 2. Use three repetitions of the Newton-Raphson algorithm to approximate (3)√(5) Enter just a real number rounded off to two decimal places (no label).

12) Use three repetitions of the Newton-Raphson algorithm to approximate √(3). Let x0 = 4.

Enter just a real number rounded off to two decimal places.

13) Use two repetitions of the Newton-Raphson algorithm to approximate √(15).

Enter just a real number rounded off to two decimal places.

14) f(x) = x5 + x - 3 has a zero between 1 and 2 .

Use two repetitions of the Newton-Raphson algorithm to approximate this zero with x0 = 1.

Enter just a real number rounded off to two decimal places.

15) Use the Newton-Raphson algorithm with two repetitions to estimate the positive solution of sinx = (1/2)x. Use x0 = 2.

Enter just a real number rounded off to two decimal places.

16) Use the Newton-Raphson algorithm with three repetitions to approximate the zero of f(x) = ex - 2 near x = 1.

Enter just a real number rounded off to two decimal places.

17) Use the Newton-Raphson algorithm with three repetitions to approximate the zero of f(x) = cosx + x - 2 near x = 3.

Enter just a real number rounded off to two decimal places.

18) Use the Newton-Raphson algorithm with three repetitions to approximate the solution to e-x = 2 - x near x = 2.

Enter just a real number rounded off to two decimal places.

19) Use two repetitions of the Newton-Raphson algorithm to approximate the zero of f(x) = sinx - cosx near x = 0.

Enter just a real number rounded off to two decimal places.

20) Use two repetitions of the Newton-Raphson algorithm to approximate the value of x for which ex = 3x. Use x = 0 as the first approximation.

Enter just a real number rounded off to two decimal places.

Solution
5 (1 Ratings )

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