To determine To calculate: The value of x 50 applied to the function f ( x ) = 1 / x and initial guess is x 0 = 1 using Newton’s law. Explanation Given information : The function is f ( x ) = 1 / x , initial guess x 0 = 1 . Calculation: Let us consider the following function. f ( x ) = 1 x .......... ( 1 ) Let us find the approximate root of the equation by Newton’s Method explained below. Consider initial guess as x 0 . And the iteration x i + 1 = x i − f ( x i ) f ′ ( x i ) Let us differentiate equation (1) with respect tox . f ′ ( x ) = d d x ( 1 x ) = − 1 x 2 And, x 1 = x 0 − f ( x 0 ) f ′ ( x 0 ) = x 0 − − 1

3rd Edition

ISBN: 9780134696454

Author: Sauer, Tim

Publisher: Pearson,

See similar textbooks

Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the se…

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integratio…

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects th…

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Videos

Question

Chapter 1.4, Problem 12E

To determine

To calculate: The value of x50 applied to the function f(x)=1/x and initial guess is x0=1 using Newton’s law.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 1.4, Problem 11E

Chapter 1.4, Problem 13E

Students have asked these similar questions

Business discuss

Use the method of undetermined coefficients to solve the given nonhomogeneous system.X' = −1 33 −1 X + −4t2t + 2 X(t) =

5) You are purchasing a game for $30. You have a 5% off coupon and sales tax is 5%. What will your final price be? Does it matter if you take off the coupon first or add in the tax first? 6) You have ten coupons that allow you to take 10% off the sales price of a jacket, and for some strange reason, the store is going to allow you to use all ten coupons! Does this mean you get the jacket for free? Let's really think about what would happen at the checkout. First, the teller would scan the price tag on the jacket, and the computer would show the price is $100. After the teller scans the first coupon, the computer will take 10% off of $100, and show the price is $90. (Right? Think about why this is.) Then after the teller scans the second coupon, the computer will take 10% off of $90. (a) Continue this reasoning to fill in the table below showing the price of the jacket (y) after you apply x coupons. (b) Make a graph showing the price of the jacket from x = 0 to x = 10 coupons applied.…

Chapter 1 Solutions

Numerical Analysis

Ch. 1.1 - Use the Intermediate Value Theorem to find an...Ch. 1.1 - Use the Intermediate Value Theorem to find an...Ch. 1.1 - Consider the equations in Exercise 1. Apply two...Ch. 1.1 - Consider the equations in Exercise 2. Apply two...Ch. 1.1 - Consider the equation x4=x3+10 . a. Find an...Ch. 1.1 - Suppose that the Bisection Method with starting...Ch. 1.1 - Prob. 1CP Ch. 1.1 - Use the Bisection Method to find the root to eight...Ch. 1.1 - Use the Bisection Method to locate all solutions...Ch. 1.1 - Prob. 4CP

Ch. 1.1 - Prob. 5CP Ch. 1.1 - Use the Bisection Method to calculate the solution...Ch. 1.1 - Use the Bisection Method to find the two real...Ch. 1.1 - The Hilbert matrix is the nn matrix whose ijth...Ch. 1.1 - Prob. 9CP Ch. 1.1 - A planet orbiting the sun traverses an ellipse....Ch. 1.2 - Find all fixed points of the following gx . a. 3x...Ch. 1.2 - Find all fixed points of the following gx . x+63x2...Ch. 1.2 - Prob. 3E Ch. 1.2 - Show that -1, 0, and 1 are fixed points of the...Ch. 1.2 - For which of the following gx is r=3 a fixed...Ch. 1.2 - For which of the following is a fixed...Ch. 1.2 - Use Theorem 1.6 to determine whether Fixed-Point...Ch. 1.2 - Use Theorem 1.6 to determine whether Fixed-Point...Ch. 1.2 - Find each fixed point and decide whether...Ch. 1.2 - Find each fixed point and decide whether...Ch. 1.2 - Express each equation as a fixed-point problem...Ch. 1.2 - Consider the Fixed-Point Iteration xgx=x20.24 ....Ch. 1.2 - (a) Find all fixed points of. (b) To which of the...Ch. 1.2 - Which of the following three Fixed-Point...Ch. 1.2 - Which of the following three Fixed-Point...Ch. 1.2 - Which of the following three Fixed-Point...Ch. 1.2 - Check that and -1 are roots of. Isolate the term...Ch. 1.2 - Prove that the method of Example 1.6 will...Ch. 1.2 - Explore the idea of Example 1.6 for cube roots. Lf...Ch. 1.2 - Improve the cube root algorithm of Exercise 19 by...Ch. 1.2 - Prob. 21E Ch. 1.2 - Prob. 22E Ch. 1.2 - Assume that gx is continuously differentiable and...Ch. 1.2 - Assume that g is a continuously differentiable...Ch. 1.2 - Prob. 25E Ch. 1.2 - Prove that a continuously differentiable function ...Ch. 1.2 - Prob. 27E Ch. 1.2 - Prob. 28E Ch. 1.2 - Prob. 29E Ch. 1.2 - Prob. 30E Ch. 1.2 - Prob. 31E Ch. 1.2 - Find the set of all initial guesses for which the...Ch. 1.2 - Prob. 33E Ch. 1.2 - Prob. 1CP Ch. 1.2 - Prob. 2CP Ch. 1.2 - Calculate the square roots of the following...Ch. 1.2 - Calculate the cube roots of the following numbers...Ch. 1.2 - Prob. 5CP Ch. 1.2 - Prob. 6CP Ch. 1.2 - Prob. 7CP Ch. 1.3 - Find the forward and backward error for the...Ch. 1.3 - Find the forward and backward error for the...Ch. 1.3 - (a) Find the multiplicity of the root r=0 of...Ch. 1.3 - (a) Find the multiplicity of the root of. (b)...Ch. 1.3 - Find the relation between forward and backward...Ch. 1.3 - Let be a positive integer. The equation defining...Ch. 1.3 - Let be the Wilkinson polynomial. (a) Prove that ...Ch. 1.3 - Let fx=xnaxn1 , and set gx=xn . (a) Use the...Ch. 1.3 - Prob. 1CP Ch. 1.3 - Carry' out Computer Problem 1 for fx=sinx3x3 .Ch. 1.3 - Prob. 3CP Ch. 1.3 - Prob. 4CP Ch. 1.3 - Prob. 5CP Ch. 1.3 - Prob. 6CP Ch. 1.4 - Apply two steps of Newton’s Method with initial...Ch. 1.4 - Apply two steps of Newton’s Method with initial...Ch. 1.4 - Use Theorem 1.11 or 1.12 to estimate the error...Ch. 1.4 - Estimate as in Exercise 3. (a) ; , (b) ; , Ch. 1.4 - Consider the equation 8x412x3+6x2x=0 . For each of...Ch. 1.4 - Sketch a function f and initial guess for which...Ch. 1.4 - Let fx=x47x3+18x220x+8 . Does Newton’s Method...Ch. 1.4 - Prove that Newton’s Method applied to fx=ax+b...Ch. 1.4 - Show that applying Newton’s Method to fx=x2A...Ch. 1.4 - Find the Fixed-Point Iteration produced by...Ch. 1.4 - Use Newton’s Method to produce a quadratically...Ch. 1.4 - Suppose Newton’s Method is applied to the...Ch. 1.4 - (a) The function has a root at . If the error ...Ch. 1.4 - Let denote the Newton’s Method iteration for the...Ch. 1.4 - Each equation has one root. Use Newton’s Method to...Ch. 1.4 - Prob. 2CP Ch. 1.4 - Apply Newton’s Method to find the only root to as...Ch. 1.4 - Carry out the steps of Computer Problem 3 for (a)...Ch. 1.4 - Prob. 5CP Ch. 1.4 - Prob. 6CP Ch. 1.4 - Consider the function fx=esin3x+x62x4x31 on the...Ch. 1.4 - Prob. 8CP Ch. 1.4 - Prob. 9CP Ch. 1.4 - Set fx=54x6+45x5102x469x3+35x2+16x4 . Plot the...Ch. 1.4 - The ideal gas law for a gas at low temperature and...Ch. 1.4 - Prob. 12CP Ch. 1.4 - Prob. 13CP Ch. 1.4 - Prob. 14CP Ch. 1.4 - Prob. 15CP Ch. 1.4 - Prob. 16CP Ch. 1.4 - Consider the national population growth model...Ch. 1.5 - Prob. 1E Ch. 1.5 - Apply two steps of the Method of False Position...Ch. 1.5 - Apply two steps of Inverse Quadratic Interpolation...Ch. 1.5 - A commercial fisher wants to set the net at a...Ch. 1.5 - Prob. 5E Ch. 1.5 - If the Secant Method converges to, , and , then...Ch. 1.5 - Consider the following four methods for...Ch. 1.5 - Prob. 1CP Ch. 1.5 - Use the Method of False Position to find the...Ch. 1.5 - Prob. 3CP Ch. 1.5 - Prob. 4CP Ch. 1.5 - Prob. 5CP Ch. 1.5 - Prob. 6CP Ch. 1.5 - Write a MATLAB function file for f . The...Ch. 1.5 - Plot f on , . You may use the @ symbol as...Ch. 1.5 - Reproduce Figure 1.15. The MATLAB commands and...Ch. 1.5 - Solve the forward kinematics problem for the...Ch. 1.5 - Prob. 5SA Ch. 1.5 - Find a strut length p2 , with the rest of the...Ch. 1.5 - Calculate the intervals in p2 , with the rest of...Ch. 1.5 - Prob. 8SA

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.