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(a). Use the numbers (called nodes) Xo = 2.0, x1 = 2.4, and x2 = 2.6...
Question 3 ( 14 Points) (a). Use the numbers (called nodes) Xo = 2.0, x1 =...
Question 3 ( 14 Points) (a). Use the numbers (called nodes) Xo = 2.0, x1 = 2.4, and x2 = 2.6 to find the second Lagrange interpolating polynomial for f(x) = sin(In x). Using 4-digit rounding arithmatic. (b). Use this polynomial to approximate f(1). Using 4-digit rounding arithmatic.
(1) Use the Bisection method to find solutions accurate to within 10-2 for x3 – 7x2...
(1) Use the Bisection method to find solutions accurate to within 10-2 for x3 – 7x2 + 14x – 6 = 0 on the interval [3.2, 4]. Using 4-digit rounding arithmatic. (2) Consider the function f(x) = cos X – X. (a). Approximate a root of f(x) using Fixed- point method accurate to within 10-2 . (b). Approximate a root of f(x) using Newton's method accurate to within 10-2. Find the second Taylor polynomial P2(x) for the function f(x) =...
Find the second Taylor polynomial P2(x) for the function f(x) = ex cos x about xo...
Find the second Taylor polynomial P2(x) for the function f(x) = ex cos x about xo = 0. Using 4-digit rounding arithmatic. (a). Use P2(0.7) to approximate f(0.7). (b). Find the actual error. (c). Find a bound for the error |f(x) – P2(x) in using P2(x) to approximate f(x) on the interval [0, 1].
Question 4 (16 Points) Use Neville's method to approximate V11 with the following function and values....
Question 4 (16 Points) Use Neville's method to approximate V11 with the following function and values. Use this polynomial to approximate f(11). Using 4-digit rounding arithmatic. (a). f(x) = (x and the values Xo = 6, xı = 8, x2 = 10, x3 = 12 and X4 = 13. (b). Compare the accuracy of the approximation in parts (a).
Question 1 (20 Points) Find the second Taylor polynomial P2(x) for the function f(x) = ex...
Question 1 (20 Points) Find the second Taylor polynomial P2(x) for the function f(x) = ex cos x about Xo = 0. Using 4-digit rounding arithmatic. (a). Use P2(0.7) to approximate f(0.7). (b). Find the actual error. (c). Find a bound for the error f(x) - P2(x) in using P2(x) to approximate f(x) on the interval [0, 1].
2019-Numerical Analysis- Quiz-2 1. Let f()-( (a) Use quadratic Lagrange interpolation based on th...
2019-Numerical Analysis- Quiz-2 1. Let f()-( (a) Use quadratic Lagrange interpolation based on the nodes xo 1, x 2, (given e 2.7183, e 7.3891, e 12.1825) f(1.2). a and x 2.5 to approximate f (1.5) and (b) Use cubic Lagrange interpolation based on the nodes xo=0.5, x1 =1, x2 = 2 and x, = 2.5 to approximate f(1.5) and f(12)
2019-Numerical Analysis- Quiz-2 1. Let f()-( (a) Use quadratic Lagrange interpolation based on the nodes xo 1, x 2, (given...
a) Solve the following problem using Lagrange multiplier method. Minimize fCX)-x1+ x2+X 4. subject to: x2+x-3...
a) Solve the following problem using Lagrange multiplier method. Minimize fCX)-x1+ x2+X 4. subject to: x2+x-3 X1+3x2+ 2x)- 7 (1) (2) (Note: Please do not check the second order sufficiency conditions) b) If the right side of the above constraint (1) is changed to 3.4, using sensitivity analysis find the approximate new minimum value of fX).
a) Solve the following problem using Lagrange multiplier method. Minimize fCX)-x1+ x2+X 4. subject to: x2+x-3 X1+3x2+ 2x)- 7 (1) (2) (Note: Please do...
Please answer every part and show formulas you have used. Will give upvote for good answer Lagrange Polynomial Study Qu...
Please answer every part and show formulas you have used. Will
give upvote for good answer
Lagrange Polynomial Study Questions Example: For given f(x) - sin3x function input-output table is given as below. Find second order Lagrange interpolating polynomial for f(x) using input-output table a. b. Find the f(1,5) value using second order Lagrange interpolating polynomial (Find Lo(x), Lix), and L2(x)) calculate f(x)-sin3x for x:1,5 using your calculator and compare case b result using c. absolute error calculation. (Hint: Use...
where x is in radians. Use Guadra tic lagrange interpolation bas ed on the nodles Xo 0.x0.5 and xz-lo to...
where x is in radians. Use Guadra tic lagrange interpolation bas ed on the nodles Xo 0.x0.5 and xz-lo to apporimate f(os and fll.2) Construct the Divided- Difference lable basedl an the node xo 1.x- 2,X2-4and x3-t, andl find the Newton Polynomial based on xo, Xiandx xk yk 2 6 5
where x is in radians. Use Guadra tic lagrange interpolation bas ed on the nodles Xo 0.x0.5 and xz-lo to apporimate f(os and fll.2)
Construct the Divided- Difference lable...
Question 2 (20 Points) (1) Use the Bisection method to find solutions accurate to within 10-2...
Question 2 (20 Points) (1) Use the Bisection method to find solutions accurate to within 10-2 for x3 - 7x2 + 14x - 6 = 0 on the interval [3.2, 4]. Using 4-digit rounding arithmatic. (2) Consider the function f(x) = cos x - x. (a). Approximate a root of f(x) using Fixed-point method accurate to within 10-2 (b). Approximate a root of f(x) using Newton's method accurate to within 10-2.
Question 3 ( 14 Points) (a). Use the numbers (called nodes) Xo = 2.0, x1 = 2.4, and x2 = 2.6 to find the second Lagrange interpolating polynomial for f(x) = sin(In x). Using 4-digit rounding arithmatic. (b). Use this polynomial to approximate f(1). Using 4-digit rounding arithmatic.
(1) Use the Bisection method to find solutions accurate to within 10-2 for x3 – 7x2 + 14x – 6 = 0 on the interval [3.2, 4]. Using 4-digit rounding arithmatic. (2) Consider the function f(x) = cos X – X. (a). Approximate a root of f(x) using Fixed- point method accurate to within 10-2 . (b). Approximate a root of f(x) using Newton's method accurate to within 10-2. Find the second Taylor polynomial P2(x) for the function f(x) =...
Find the second Taylor polynomial P2(x) for the function f(x) = ex cos x about xo = 0. Using 4-digit rounding arithmatic. (a). Use P2(0.7) to approximate f(0.7). (b). Find the actual error. (c). Find a bound for the error |f(x) – P2(x) in using P2(x) to approximate f(x) on the interval [0, 1].
Question 4 (16 Points) Use Neville's method to approximate V11 with the following function and values. Use this polynomial to approximate f(11). Using 4-digit rounding arithmatic. (a). f(x) = (x and the values Xo = 6, xı = 8, x2 = 10, x3 = 12 and X4 = 13. (b). Compare the accuracy of the approximation in parts (a).
Question 1 (20 Points) Find the second Taylor polynomial P2(x) for the function f(x) = ex cos x about Xo = 0. Using 4-digit rounding arithmatic. (a). Use P2(0.7) to approximate f(0.7). (b). Find the actual error. (c). Find a bound for the error f(x) - P2(x) in using P2(x) to approximate f(x) on the interval [0, 1].
2019-Numerical Analysis- Quiz-2 1. Let f()-( (a) Use quadratic Lagrange interpolation based on the nodes xo 1, x 2, (given e 2.7183, e 7.3891, e 12.1825) f(1.2). a and x 2.5 to approximate f (1.5) and (b) Use cubic Lagrange interpolation based on the nodes xo=0.5, x1 =1, x2 = 2 and x, = 2.5 to approximate f(1.5) and f(12)
2019-Numerical Analysis- Quiz-2 1. Let f()-( (a) Use quadratic Lagrange interpolation based on the nodes xo 1, x 2, (given...
a) Solve the following problem using Lagrange multiplier method. Minimize fCX)-x1+ x2+X 4. subject to: x2+x-3 X1+3x2+ 2x)- 7 (1) (2) (Note: Please do not check the second order sufficiency conditions) b) If the right side of the above constraint (1) is changed to 3.4, using sensitivity analysis find the approximate new minimum value of fX).
a) Solve the following problem using Lagrange multiplier method. Minimize fCX)-x1+ x2+X 4. subject to: x2+x-3 X1+3x2+ 2x)- 7 (1) (2) (Note: Please do...
Please answer every part and show formulas you have used. Will
give upvote for good answer
Lagrange Polynomial Study Questions Example: For given f(x) - sin3x function input-output table is given as below. Find second order Lagrange interpolating polynomial for f(x) using input-output table a. b. Find the f(1,5) value using second order Lagrange interpolating polynomial (Find Lo(x), Lix), and L2(x)) calculate f(x)-sin3x for x:1,5 using your calculator and compare case b result using c. absolute error calculation. (Hint: Use...
where x is in radians. Use Guadra tic lagrange interpolation bas ed on the nodles Xo 0.x0.5 and xz-lo to apporimate f(os and fll.2) Construct the Divided- Difference lable basedl an the node xo 1.x- 2,X2-4and x3-t, andl find the Newton Polynomial based on xo, Xiandx xk yk 2 6 5
where x is in radians. Use Guadra tic lagrange interpolation bas ed on the nodles Xo 0.x0.5 and xz-lo to apporimate f(os and fll.2)
Construct the Divided- Difference lable...
Question 2 (20 Points) (1) Use the Bisection method to find solutions accurate to within 10-2 for x3 - 7x2 + 14x - 6 = 0 on the interval [3.2, 4]. Using 4-digit rounding arithmatic. (2) Consider the function f(x) = cos x - x. (a). Approximate a root of f(x) using Fixed-point method accurate to within 10-2 (b). Approximate a root of f(x) using Newton's method accurate to within 10-2.
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