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answer is shown in bold, please show steps to get answer <13 > Use the method of undetermined coefficients to derive an approximation for the second derivative of the following form and fin...
1. Use the method of undetermined coefficients to compute the coefficients of a finite difference approximation...
1. Use the method of undetermined coefficients to compute the coefficients of a finite difference approximation for u'(E) using the values u(0),u (1) and u(2). Choose the coefficients such that the formula is exact for polynomials with degree less or equal to 2. Can you use these ecoefficients to get an approximation for a first derivative based on function values v(r),v(x+h)and v(x +2h)? At which point z and for which functions v(a) is this approximation equal to '()? Determine the...
Derive the following numerical approximation to the second derivative of f(x) using Taylor's series. Show all...
Derive the following numerical approximation to the second derivative of f(x) using Taylor's series. Show all of your steps and derive also the order of accuracy of this approximation in terms of h. - f(x + 2h) + 16f(x + h) – 30f(x) + 16 f(x – h) – f(x – 2h) 12h2 1 (C)
4. Given a function f(x), use Taylor approximations to derive a second order one-sided ap- proximation to f'(ro...
4. Given a function f(x), use Taylor approximations to derive a second order one-sided ap- proximation to f'(ro) is given by f(zo + h) + cf (zo + 21) + 0(h2). f' (zo) = af(xo) + What is the precise form of the error term? Using the formula approximate f' (1) where r) = e* for h 1/(2p) for p = 1 : 15, Form a table with columns giving h, the approximation, absolute error and absolute error divided by...
please assist 4. (25 pts) Consider a forward-difference approximation for the second derivative of the form Use Taylor's theorem to determine the coefficients A, B, and C that give the maximal...
please assist
4. (25 pts) Consider a forward-difference approximation for the second derivative of the form Use Taylor's theorem to determine the coefficients A, B, and C that give the maximal order of accuracy and determine what this order is.
4. (25 pts) Consider a forward-difference approximation for the second derivative of the form Use Taylor's theorem to determine the coefficients A, B, and C that give the maximal order of accuracy and determine what this order is.
Please show all work Use method of undetermined coefficients to determine the appropriate form of a...
Please show all work
Use method of undetermined coefficients to determine the appropriate form of a par- ticular solution yp (1) of the differential equation: y" + 4y + 4y = 2.re 2 + 8 sin (2.c). (Do NOT solve for the coefficients constants).
Find the general solution of y'' + y'-6y=(9x-2)e^(2x). (Use the method of undetermined coefficients) Please show...
Find the general solution of y'' + y'-6y=(9x-2)e^(2x).
(Use the method of undetermined coefficients)
Please show all work and steps!
2. Find a general solution of y" + y' - 6y = (9.C -- 2)e2.. (22 p'ts, use the method of undeter- mined coefficients.)
Using the Method of Undetermined Coefficients, determine the form of a particular solution for the differential...
Using the Method of Undetermined Coefficients, determine the form of a particular solution for the differential equation. (Do not evaluate coefficients.). y" - 18y + 81y = 17691 What are the roots of the auxiliary equation associated with the given differential equation? The associated auxiliary equation has the two roots ОА. (Use a comma to separate answers as needed.) OB. The associated auxiliary equation has the double root OC. There are no roots to the associated auxiliary equation Write the...
answer all thee questions with work!!! please and Thank you (1) Find the derivative of each...
answer all thee questions with work!!! please and Thank you
(1) Find the derivative of each of the following functions: (a) f(t) = ln(3-cost) (6) gle) = VERA (2) (a) Find the linear approximation to y-Vaata 81. (b) Use your answer in (a) to approximate V80. (All work must be shown it is not enough to put this into a calculator!) (3) Find the absolute maximum and minimum of the function h(x) = x + on the interval (0.1, 4).
2. (20 pts) Consider the following function with its second derivative in simplified form (you should...
2. (20 pts) Consider the following function with its second derivative in simplified form (you should compute the first derivative): 4.2 f(x) = x²+1 f"(x) = 8.2(x - 3)(x + 3) (x² + 13 "None" could be an appropriate answer for some of the statements below: (a) (2 pts) The domain of f(x) is (b) (2 pts) An x-intercept of the graph of y = f(x) occurs at x = (c) (2 pts) The graph of y = f(x) has...
Please write the steps, thanks. 13. a. Approximate the given quantity using a Taylor polynomial with n b. Compute the absolute error in the approximation assuming the exact value is given by a cal...
Please write the steps, thanks.
13. a. Approximate the given quantity using a Taylor polynomial with n b. Compute the absolute error in the approximation assuming the exact value is given by a calculator 3. 266 a. P3 (266) (Do not round until the final answer. Then round to five decimal places as needed.) b. absolute error se scientific notation. Use the multiplication symbol in the math palette as needed. Do not round until the final answer. Then round to...
1. Use the method of undetermined coefficients to compute the coefficients of a finite difference approximation for u'(E) using the values u(0),u (1) and u(2). Choose the coefficients such that the formula is exact for polynomials with degree less or equal to 2. Can you use these ecoefficients to get an approximation for a first derivative based on function values v(r),v(x+h)and v(x +2h)? At which point z and for which functions v(a) is this approximation equal to '()? Determine the...
Derive the following numerical approximation to the second derivative of f(x) using Taylor's series. Show all of your steps and derive also the order of accuracy of this approximation in terms of h. - f(x + 2h) + 16f(x + h) – 30f(x) + 16 f(x – h) – f(x – 2h) 12h2 1 (C)
4. Given a function f(x), use Taylor approximations to derive a second order one-sided ap- proximation to f'(ro) is given by f(zo + h) + cf (zo + 21) + 0(h2). f' (zo) = af(xo) + What is the precise form of the error term? Using the formula approximate f' (1) where r) = e* for h 1/(2p) for p = 1 : 15, Form a table with columns giving h, the approximation, absolute error and absolute error divided by...
please assist
4. (25 pts) Consider a forward-difference approximation for the second derivative of the form Use Taylor's theorem to determine the coefficients A, B, and C that give the maximal order of accuracy and determine what this order is.
4. (25 pts) Consider a forward-difference approximation for the second derivative of the form Use Taylor's theorem to determine the coefficients A, B, and C that give the maximal order of accuracy and determine what this order is.
Please show all work
Use method of undetermined coefficients to determine the appropriate form of a par- ticular solution yp (1) of the differential equation: y" + 4y + 4y = 2.re 2 + 8 sin (2.c). (Do NOT solve for the coefficients constants).
Find the general solution of y'' + y'-6y=(9x-2)e^(2x).
(Use the method of undetermined coefficients)
Please show all work and steps!
2. Find a general solution of y" + y' - 6y = (9.C -- 2)e2.. (22 p'ts, use the method of undeter- mined coefficients.)
Using the Method of Undetermined Coefficients, determine the form of a particular solution for the differential equation. (Do not evaluate coefficients.). y" - 18y + 81y = 17691 What are the roots of the auxiliary equation associated with the given differential equation? The associated auxiliary equation has the two roots ОА. (Use a comma to separate answers as needed.) OB. The associated auxiliary equation has the double root OC. There are no roots to the associated auxiliary equation Write the...
answer all thee questions with work!!! please and Thank you
(1) Find the derivative of each of the following functions: (a) f(t) = ln(3-cost) (6) gle) = VERA (2) (a) Find the linear approximation to y-Vaata 81. (b) Use your answer in (a) to approximate V80. (All work must be shown it is not enough to put this into a calculator!) (3) Find the absolute maximum and minimum of the function h(x) = x + on the interval (0.1, 4).
2. (20 pts) Consider the following function with its second derivative in simplified form (you should compute the first derivative): 4.2 f(x) = x²+1 f"(x) = 8.2(x - 3)(x + 3) (x² + 13 "None" could be an appropriate answer for some of the statements below: (a) (2 pts) The domain of f(x) is (b) (2 pts) An x-intercept of the graph of y = f(x) occurs at x = (c) (2 pts) The graph of y = f(x) has...
Please write the steps, thanks.
13. a. Approximate the given quantity using a Taylor polynomial with n b. Compute the absolute error in the approximation assuming the exact value is given by a calculator 3. 266 a. P3 (266) (Do not round until the final answer. Then round to five decimal places as needed.) b. absolute error se scientific notation. Use the multiplication symbol in the math palette as needed. Do not round until the final answer. Then round to...
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