6. (25 pts) Find the osculating polynomial, P, interpolating the following table of data, and evaluate...
4. For the following table, answer the questions. (1) Find the cubic Newton’s interpolating polynomial using the first four data points and estimate the function value at x=2.5 with the interpolating polynomial. (2) Find the quartic Newton’s interpolating polynomial using the five data points and estimate the function value at x=2.5 with the interpolating polynomial. (3) Find the bases functions of Lagrange interpolation, Li(x) (i=1,2,…,5), and estimate the function value at x=2.5 with the Lagrange interpolating polynomial. 3 5 1...
Given the data points (-3,5),(-2,5),(-1,3), (0, 1) (a) Find the interpolating polynomial passing through these points. (b) Using your polynomial from (a), evaluate P(1). (c) This polynomial interpolates the function f(x) = 24. Find an upper bound for the approximation in part (b).
Complete the Divided difference table and construct the interpolating polynomial that uses the data given in column 2 and column 3. f [x j-1, xi] f [x 1-2, X j-1, x ] f [x i-. ......, xi] f [x 14......., xi] i xi f[xi] 01.00.7751866 | 1 | 1.20.5900775 21.70.4534024 31. 90.2829184 4 2.3 0.1204522
12. Given the data set: We want to find the interpolating polynomial of degree 2 through these points. a) Write the interpolating polynomial in Lagrange form b) Write the interpolating polynomial in Newton form.
(a) Find the degree 1 interpolating P(x) through the points (a, f(a)) and (b, f(b)) (b) Develop the following formula by using the interpolating polynomial P1 (x), (c) Find the degree of precision of the approximation, T1 (f) = f(1) + f(-1), for f(r)dr. (a) Find the degree 1 interpolating P(x) through the points (a, f(a)) and (b, f(b)) (b) Develop the following formula by using the interpolating polynomial P1 (x), (c) Find the degree of precision of the approximation,...
1. Consider Shamir's Lagrange interpolating polynomial key threshold scheme. Let t p-11, K-Tand Compute shadows for 1, 2, 3, 4, 5, 6 and 7. Reconstruct h(x) from the shadows for x-1, 3, 5 and 7. 1. Consider Shamir's Lagrange interpolating polynomial key threshold scheme. Let t p-11, K-Tand Compute shadows for 1, 2, 3, 4, 5, 6 and 7. Reconstruct h(x) from the shadows for x-1, 3, 5 and 7.
Compute, using divided differences, the value of the piecewise cubic Her- mite interpolating polynomial at x = 11=10 given nodes at xi = i, for i = 1; : : : ; 10, and values and derivatives at the nodes from the function f(x) = 1=x. Remember iterative formula for divided differences: 2. (25 pts) Compute, using divided differences, the value of the piecewise cubic Her mite interpolating polynomial at x-11/10 given nodes at ai-i, for i-1, , 10. and...
Consider the following table of data points: Using least squares fitting, find the polynomial Q(x) of degree 2 that fits the data points given in the table above. Approximate f(0.3) using Q(0.3). Use P(x) = Ax2+Bx +C to find 3 equations and then find A,B,C. f(x) i Xi 0 0.000 1.00000 1 0.125 0.98450 2 0.250 0.93941 0.375 0.86882 4 0.500 0.77880 5 0.625 0.67663 6 0.750 0.56978 0.875 0.46504 8 1.000 0.36788
(6 pts) (11) Find the domain and range of the function (x) - 3 - 25 - x (Hint: Graph it.) (4 pts) (12) Suppose that f(x) - (X-4 XS2 X > 2 Evaluate each of the following: (a) f(-5) (b) f(5) (8 pts) (13) If h(x) = 5x73, find h'(x). pts) (14) Find an equation of the parabola with vertex (5. --3) and which passes through the point (2.4)
3) A 2nd-order Lagrange Interpolating Polynomial is to be fit to the following data points:(1)-1,1(2)4, 1(3)-9. Determine the polynomial term corresponding to the data point f(3) 8. Be sure to simplify as much as possible. (Don't take time to write the other two terms.) (1 point)