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Question 3 (a) Grven that f(-2)= 46, f(-1) 4, J(1) 1, f(3)= 156, and f(4)= 484, formula to estimate f(0) Use four-d...
Consider the following data table: 0 2i = 0.2 0.4 f(xi) = 2 2.018 2.104 2.306...
Consider the following data table: 0 2i = 0.2 0.4 f(xi) = 2 2.018 2.104 2.306 0.6 0.2 and 23=0.4 is The linear Lagrange interpolator L1,1 (2) used to linearly interpolate between data points 12 (Chop after 2 decimal places) None of the above. -2.50x+0.20 -5.00x+2.00 -5.00x+2.00 5.00x-1.00 Consider the following data table: 2 Ti = 0 0.2 0.4 0.6 f(x) = 2.018 2.104 2.306 0.2 and 23 = 0.4, the value obtained at 2=0.3 is Using Lagrange linear interpolation...
3. (30 points) Let f(x) = 1/x and data points Zo = 2, x,-3 and x2 = 4. Note that you can use the ...
3. (30 points) Let f(x) = 1/x and data points Zo = 2, x,-3 and x2 = 4. Note that you can use the abscissae to find the corresponding ordinates (a) (8 points) Find by hand the Lagrange form, the standard form, and the Newton form of the interpolating polynomial p2(x) of f(x) at the given points. State which is which! Then, expand out the Newton and Lagrange form to verify that they agree with the standard form of p2...
8. Use divided differences to find the interpolation polynomial for the data f (x)-1 -3 -2 4 f' (x) f"(x) 8. Use divided differences to find the interpolation polynomial for the data f (...
8. Use divided differences to find the interpolation polynomial for the data f (x)-1 -3 -2 4 f' (x) f"(x)
8. Use divided differences to find the interpolation polynomial for the data f (x)-1 -3 -2 4 f' (x) f"(x)
L-8 29 -15 22] 111 4 3 2 1 10. The differential equations of high order: 2 And boundary conditions fo)-0, f' (0)-0, f'(5)-1, g(o)-1.5, g(5)-1 Can be solved using The Shooting-Newton-Raphson a...
L-8 29 -15 22] 111 4 3 2 1 10. The differential equations of high order: 2 And boundary conditions fo)-0, f' (0)-0, f'(5)-1, g(o)-1.5, g(5)-1 Can be solved using The Shooting-Newton-Raphson and multivariable Runge-Kutta for a value of (y-1.7), re write the system of equations in the canonical form (i.e. as a set of ODES of first order and its boundary conditions). It is not required to solve the equations, just list the system of first order differential equations...
Co OCT/SOV013 Question 3 () Conesdes the data 0 25 00 Consa wct the drvaled daference s Lable for the data (2) () Co...
Co OCT/SOV013 Question 3 () Conesdes the data 0 25 00 Consa wct the drvaled daference s Lable for the data (2) () Consrwet the Newton forsn of the polynomsnl p(a) of lowe-t degree that tes polates /) nt these potse () (n) Suppose that these data wese generated by thhe fumton cos 21 J)-1 2 Use the nest term rule to appOInate the eror Ipl)-f)over the intessal 0,05 Your anves should be a numbes (3) (b) Let f)Co +ealco...
Exercise 6: Given the table of the function f(x)-2" 2 X 0 3 2 f(x) 1 2 4 8 a) Write down the Newton polynomial...
Exercise 6: Given the table of the function f(x)-2" 2 X 0 3 2 f(x) 1 2 4 8 a) Write down the Newton polynomials P1(x), P2(x), Pa(x). b) Evaluate f(2.5) by using Pa(x). c) Obtain a bound for the errors E1(x), E2(x), Es(x) Exercise 7: Consider f(x)- In(x) use the following formula to answer the given questions '(x) +16-30f+16f,- 12h a) Derive the numerical differentiation formula using Taylor Series and find the truncation error b) Approximate f'(1.2) with h-0.05...
2 6, 9、19/ 1,12 '12,13,16,16, 16,18,3‘ = 12.5 4 IQR=46 Question #1 (15 Marks) a) (8 Marks) Answer the following questions with True or False. 1) Every basic solution in the assignment p...
2 6, 9、19/ 1,12 '12,13,16,16, 16,18,3‘ = 12.5 4 IQR=46 Question #1 (15 Marks) a) (8 Marks) Answer the following questions with True or False. 1) Every basic solution in the assignment problem is necessarily degenerate. 2) The assignment problem cannot be solved using the transportation technique. maximum or minimum. If a single-variable function has two local minima, it must have at least one local 4) maximum. 5) The Golden Section Search method gives better results than the Fibanocci Search...
Consider the simple graph G, given the following: (assume A=0,B=1, C=2, D=3, E=4, F=5, G=6) A...
Consider the simple graph G, given the following: (assume A=0,B=1, C=2, D=3, E=4, F=5, G=6) A 3 3 8 B D 5 ho 5 8 E F G 4 3 a) Use the Breadth-First Search algorithm to traverse G and give the traverse sequence, starting from A. Assume you always choose the candidate with the SMALLEST index among the candidates at each step. b) Use the Depth-First Search algorithm to traverse G and give the traverse sequence, starting from A....
B D E F G 1 40,000 Year 2 Quarter 2 3 60,000 100,000 4 50,000...
B D E F G 1 40,000 Year 2 Quarter 2 3 60,000 100,000 4 50,000 Year 3 Quarter 1 2 70,000 80,000 A 2 Master Budget: Excel Sheet 2 3 Data 4 5 Budgeted unit sales 6 7 . Selling price per unit 8 • Accounts receivable, beginning balance 9 • Sales collected in the quarter sales are made 10 - Sales collected in the quarter after sales are made 11 • Desired ending finished goods inventory is 12...
Let gx)- t) dt, where f is the function whose graph is shown (a) Evaluate gtx) for x - 0, 1, 2, 3, 4, 5, and 6 gt1)-1/2 0t2)-0 g(3) - -1/2 ot4)-0 9(5)-3/2 9(6)-4 (b) Estimate g(7). (Use the midpo...
Let gx)- t) dt, where f is the function whose graph is shown (a) Evaluate gtx) for x - 0, 1, 2, 3, 4, 5, and 6 gt1)-1/2 0t2)-0 g(3) - -1/2 ot4)-0 9(5)-3/2 9(6)-4 (b) Estimate g(7). (Use the midpoint to get the most precise estimate.) 9(7)- (c) Where does g have a maximum and a minimum value? minimumx maximum x (d) Sketch a rough graph of g.
Let gx)- t) dt, where f is the function whose graph...
Consider the following data table: 0 2i = 0.2 0.4 f(xi) = 2 2.018 2.104 2.306 0.6 0.2 and 23=0.4 is The linear Lagrange interpolator L1,1 (2) used to linearly interpolate between data points 12 (Chop after 2 decimal places) None of the above. -2.50x+0.20 -5.00x+2.00 -5.00x+2.00 5.00x-1.00 Consider the following data table: 2 Ti = 0 0.2 0.4 0.6 f(x) = 2.018 2.104 2.306 0.2 and 23 = 0.4, the value obtained at 2=0.3 is Using Lagrange linear interpolation...
3. (30 points) Let f(x) = 1/x and data points Zo = 2, x,-3 and x2 = 4. Note that you can use the abscissae to find the corresponding ordinates (a) (8 points) Find by hand the Lagrange form, the standard form, and the Newton form of the interpolating polynomial p2(x) of f(x) at the given points. State which is which! Then, expand out the Newton and Lagrange form to verify that they agree with the standard form of p2...
8. Use divided differences to find the interpolation polynomial for the data f (x)-1 -3 -2 4 f' (x) f"(x)
8. Use divided differences to find the interpolation polynomial for the data f (x)-1 -3 -2 4 f' (x) f"(x)
L-8 29 -15 22] 111 4 3 2 1 10. The differential equations of high order: 2 And boundary conditions fo)-0, f' (0)-0, f'(5)-1, g(o)-1.5, g(5)-1 Can be solved using The Shooting-Newton-Raphson and multivariable Runge-Kutta for a value of (y-1.7), re write the system of equations in the canonical form (i.e. as a set of ODES of first order and its boundary conditions). It is not required to solve the equations, just list the system of first order differential equations...
Co OCT/SOV013 Question 3 () Conesdes the data 0 25 00 Consa wct the drvaled daference s Lable for the data (2) () Consrwet the Newton forsn of the polynomsnl p(a) of lowe-t degree that tes polates /) nt these potse () (n) Suppose that these data wese generated by thhe fumton cos 21 J)-1 2 Use the nest term rule to appOInate the eror Ipl)-f)over the intessal 0,05 Your anves should be a numbes (3) (b) Let f)Co +ealco...
Exercise 6: Given the table of the function f(x)-2" 2 X 0 3 2 f(x) 1 2 4 8 a) Write down the Newton polynomials P1(x), P2(x), Pa(x). b) Evaluate f(2.5) by using Pa(x). c) Obtain a bound for the errors E1(x), E2(x), Es(x) Exercise 7: Consider f(x)- In(x) use the following formula to answer the given questions '(x) +16-30f+16f,- 12h a) Derive the numerical differentiation formula using Taylor Series and find the truncation error b) Approximate f'(1.2) with h-0.05...
2 6, 9、19/ 1,12 '12,13,16,16, 16,18,3‘ = 12.5 4 IQR=46 Question #1 (15 Marks) a) (8 Marks) Answer the following questions with True or False. 1) Every basic solution in the assignment problem is necessarily degenerate. 2) The assignment problem cannot be solved using the transportation technique. maximum or minimum. If a single-variable function has two local minima, it must have at least one local 4) maximum. 5) The Golden Section Search method gives better results than the Fibanocci Search...
Consider the simple graph G, given the following: (assume A=0,B=1, C=2, D=3, E=4, F=5, G=6) A 3 3 8 B D 5 ho 5 8 E F G 4 3 a) Use the Breadth-First Search algorithm to traverse G and give the traverse sequence, starting from A. Assume you always choose the candidate with the SMALLEST index among the candidates at each step. b) Use the Depth-First Search algorithm to traverse G and give the traverse sequence, starting from A....
B D E F G 1 40,000 Year 2 Quarter 2 3 60,000 100,000 4 50,000 Year 3 Quarter 1 2 70,000 80,000 A 2 Master Budget: Excel Sheet 2 3 Data 4 5 Budgeted unit sales 6 7 . Selling price per unit 8 • Accounts receivable, beginning balance 9 • Sales collected in the quarter sales are made 10 - Sales collected in the quarter after sales are made 11 • Desired ending finished goods inventory is 12...
Let gx)- t) dt, where f is the function whose graph is shown (a) Evaluate gtx) for x - 0, 1, 2, 3, 4, 5, and 6 gt1)-1/2 0t2)-0 g(3) - -1/2 ot4)-0 9(5)-3/2 9(6)-4 (b) Estimate g(7). (Use the midpoint to get the most precise estimate.) 9(7)- (c) Where does g have a maximum and a minimum value? minimumx maximum x (d) Sketch a rough graph of g.
Let gx)- t) dt, where f is the function whose graph...
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