Explanation Given: The given function is, f ( x ) = { e − 1 / x 2 , x ≠ 0 , 0 , x = 0 Approach: The Taylor series expansion about a point x 0 is given by, f ( x ) = f ( x 0 ) + ( x − x 0 ) f ′ ( x 0 ) + ( x − x 0 ) 2 2 ! f ″ ( x 0 ) + ( x − x 0 ) 3 3 ! f ‴ ( x 0 ) + ... When x 0 = 0 the series, f ( x ) = f ( 0 ) + ( x ) f ′ ( 0 ) + ( x ) 2 2 ! f ″ ( 0 ) + ( x ) 3 3 ! f ‴ ( 0 ) + ... is said to be the Maclaurin’s series. Calculation: The given function is, f ( x ) = { e − 1 / x 2 , x ≠ 0 , 0 , x = 0 f ( 0 ) = 0

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

See similar textbooks

Videos

Question

Chapter 8.2, Problem 37E

To determine

To show:

The Maclaurin series for given f(x) is 0+0+0+..., which converges for all x but is equal to f(x) only when x=0.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.2, Problem 36E

Chapter 8.2, Problem 38E

Students have asked these similar questions

Client 1 Weight before diet (pounds) Weight after diet (pounds) 128 120 2 131 123 3 140 141 4 178 170 5 121 118 6 136 136 7 118 121 8 136 127 a) Determine the mean change in patient weight from before to after the diet (after – before). What is the 95% confidence interval of this mean difference?

You manage a chemical company with 2 warehouses. The following quantities of Important Chemical A have arrived from an international supplier at 3 different ports: Chemical Available (L) Port 1 Port 2 Port 3 400 110 100 The following amounts of Important Chemical A are required at your warehouses: Warehouse 1 Warehouse 2 Chemical Required (L) 380 230 The cost in £ to ship 1L of chemical from each port to each warehouse is as follows: Warehouse 1 Warehouse 2 Port 1 £10 £45 Port 2 £20 £28 Port 3 £13 £11 (a) You want to know how to send these shipments as cheaply as possible. For- mulate this as a linear program (you do not need to formulate it in standard inequality form) indicating what each variable represents.

a) Suppose that we are carrying out the 1-phase simplex algorithm on a linear program in standard inequality form (with 3 variables and 4 constraints) and suppose that we have reached a point where we have obtained the following tableau. Apply one more pivot operation, indicating the highlighted row and column and the row operations you carry out. What can you conclude from your updated tableau? x1 12 23 81 82 83 S4 $1 -20 1 1 0 0 0 3 82 3 0 -2 0 1 2 0 6 12 1 1 -3 0 0 1 0 2 84 -3 0 2 0 0 -1 1 4 2 -2 0 11 0 0 -4 0 -8 b) Solve the following linear program using the 2-phase simplex algorithm. You should give the initial tableau and each further tableau produced during the execution of the algorithm. If the program has an optimal solution, give this solution and state its objective value. If it does not have an optimal solution, say why. maximize 21 - - 2x2 + x3 - 4x4 subject to 2x1+x22x3x4≥ 1, 5x1+x2-x3-4 -1, 2x1+x2-x3-342, 1, 2, 3, 4 ≥0.

Chapter 8 Solutions

Fundamentals of Differential Equations and Boundary Value Problems

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.

The Maclaurin series for given f ( x ) is 0 + 0 + 0 + ... , which converges for all x but is equal to f ( x ) only when x = 0 .

Solution Summary: The author explains how the Maclaurin series for given f(x) is converged for all

Videos

To show:

The Maclaurin series for given f(x) is 0+0+0+..., which converges for all x but is equal to f(x) only when x=0.

Want to see the full answer?

Chapter 8 Solutions

The Maclaurin series for given f ( x ) is 0 + 0 + 0 + ... , which converges for all x but is equal to f ( x ) only when x = 0 .

Solution Summary: The author explains how the Maclaurin series for given f(x) is converged for all

Videos

To show: The Maclaurin series for given f(x) is 0+0+0+..., which converges for all x but is equal to f(x) only when x=0.

Want to see the full answer?

Chapter 8 Solutions

To show:

The Maclaurin series for given f(x) is 0+0+0+..., which converges for all x but is equal to f(x) only when x=0.