![Question 7. [7 points] Consider the following set of data: 0.5 1 2 y 0.4621170.761594 0.96402 a) Write down the Lagrange poly](http://img.homeworklib.com/questions/d8fa96c0-24d3-11eb-846c-fde9c664c1aa.png?x-oss-process=image/resize,w_560)
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Question 7. [7 points] Consider the following set of data: 0.5 1 2 y 0.4621170.761594 0.96402...
Consider the following data points: (0.5, 2.2), (0.75, 1.78) and (1.4, 1.51), where each point is...
Consider the following data points: (0.5, 2.2), (0.75, 1.78) and (1.4, 1.51), where each point is in the form (1;, fi), with fi = f(2) for some unknown function f. Find p2(2) with coefficients to 4 decimal places via Lagrange interpolation. Interpolate a value at r = 0.9. Given that į < f'" (c) < į on the interval (0.5, 1.4), estimate the error bounds.
12. Given the data set: We want to find the interpolating polynomial of degree 2 through...
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.
Consider the following function. (x) = x-8, (a) Approximate fby a Taylor polynomial with degree n at the number a. 0.8 s xs 1.2 n=2, a31, T2(x) = Tmx) when x lies in the given interval. (Round your a...
Consider the following function. (x) = x-8, (a) Approximate fby a Taylor polynomial with degree n at the number a. 0.8 s xs 1.2 n=2, a31, T2(x) = Tmx) when x lies in the given interval. (Round your answer to six decimal places.) (b) Use Taylor's Inequality to estimate the accuracy of the approximation rx (c) Check your result in part (b) by graphing R(x)l 3 2.5 2.0 1.2 WebAssign Plot 0.9 0.5 1.2 0.9 3 1.2 1.0 -0.5 1.0...
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...
need help doing this in matlab. 1.2-1.4 Problem #1. For five data points listed in Table...
need help doing this in matlab. 1.2-1.4
Problem #1. For five data points listed in Table 1, you are asked to do the following: Write down the form of a Newton's interpolating polynomial function of 4th-order with five constants (b, i = 1:5). 1.2 Calculate the following three divided differences (Newton bracket) (showing the detailed steps and numbers on a white paper): [xy, x,]= [xx, x,]= S[X2, x3, x,]= Plot both the data points and the interpolating function by using...
Consider the following function. /(x)=x-5, a= 1, n= 2, 0.8SXS 1.2 (a) Approximate f by a Taylor p...
Consider the following function. /(x)=x-5, a= 1, n= 2, 0.8SXS 1.2 (a) Approximate f by a Taylor polynomial with degree n at the number a T2(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation x) ~ Tn(x) when x lies in the given interval. (Round your answer to six decimal places.) (c) Check your result in part (b) by graphing Rn(x) 0.6 0.4 0.2 0.6 0.4 0.2 0.9 0.9 1.2 -0.2 -0.4 -0.6 -0.2 -0.4 -0.6...
- Question 5 1 point Number Help Given data points (x;, Y;) for j= 0,...,9, the...
- Question 5 1 point Number Help Given data points (x;, Y;) for j= 0,...,9, the degree of the Lagrange polynomial L3(x) is Number I
Question 3 (a) Consider the data. 00 0 25 0.5 05 () Construct the divaded difference's table for the data (u) Co...
Question 3 (a) Consider the data. 00 0 25 0.5 05 () Construct the divaded difference's table for the data (u) Construct the Newton form of the polynomial of lowest degree that interpolates /() at these points (3) (ii) Suppose that these data were generated by the function cos 2 ()=1+ 2 Use the next term rule to approximate the error Ip(z)- f() over the interval 0,0 5 Your answer should be a pumber 3 (b) Let F ((z) co+...
Question 17 > B0/2 pts Perform rank correlation analysis on the following data set: Y -0.5...
Question 17 > B0/2 pts Perform rank correlation analysis on the following data set: Y -0.5 14.4 11.6 20.5 1 2.8 3.7 5.3 7.2 7.8 9.7 11.1 11.7 162 19.4 16.8 25.7 38.2 The scatterplot of the data looks like this: Fill in the following table: у X-rank y-rank 1 -0.5 1 2.8 14.4 2 3.7 11.6 3 5.3 20.5 4 7.2 16.2 5 7.8 19.4 6 9.7 16.8 7 11.1 25.7 8 11.7 38.2 9 What is the rank...
3) A 2nd-order Lagrange Interpolating Polynomial is to be fit to the following data points:(1)-1,1(2)4, 1(3)-9....
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)
Consider the following data points: (0.5, 2.2), (0.75, 1.78) and (1.4, 1.51), where each point is in the form (1;, fi), with fi = f(2) for some unknown function f. Find p2(2) with coefficients to 4 decimal places via Lagrange interpolation. Interpolate a value at r = 0.9. Given that į < f'" (c) < į on the interval (0.5, 1.4), estimate the error bounds.
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.
Consider the following function. (x) = x-8, (a) Approximate fby a Taylor polynomial with degree n at the number a. 0.8 s xs 1.2 n=2, a31, T2(x) = Tmx) when x lies in the given interval. (Round your answer to six decimal places.) (b) Use Taylor's Inequality to estimate the accuracy of the approximation rx (c) Check your result in part (b) by graphing R(x)l 3 2.5 2.0 1.2 WebAssign Plot 0.9 0.5 1.2 0.9 3 1.2 1.0 -0.5 1.0...
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...
need help doing this in matlab. 1.2-1.4
Problem #1. For five data points listed in Table 1, you are asked to do the following: Write down the form of a Newton's interpolating polynomial function of 4th-order with five constants (b, i = 1:5). 1.2 Calculate the following three divided differences (Newton bracket) (showing the detailed steps and numbers on a white paper): [xy, x,]= [xx, x,]= S[X2, x3, x,]= Plot both the data points and the interpolating function by using...
Consider the following function. /(x)=x-5, a= 1, n= 2, 0.8SXS 1.2 (a) Approximate f by a Taylor polynomial with degree n at the number a T2(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation x) ~ Tn(x) when x lies in the given interval. (Round your answer to six decimal places.) (c) Check your result in part (b) by graphing Rn(x) 0.6 0.4 0.2 0.6 0.4 0.2 0.9 0.9 1.2 -0.2 -0.4 -0.6 -0.2 -0.4 -0.6...
- Question 5 1 point Number Help Given data points (x;, Y;) for j= 0,...,9, the degree of the Lagrange polynomial L3(x) is Number I
Question 3 (a) Consider the data. 00 0 25 0.5 05 () Construct the divaded difference's table for the data (u) Construct the Newton form of the polynomial of lowest degree that interpolates /() at these points (3) (ii) Suppose that these data were generated by the function cos 2 ()=1+ 2 Use the next term rule to approximate the error Ip(z)- f() over the interval 0,0 5 Your answer should be a pumber 3 (b) Let F ((z) co+...
Question 17 > B0/2 pts Perform rank correlation analysis on the following data set: Y -0.5 14.4 11.6 20.5 1 2.8 3.7 5.3 7.2 7.8 9.7 11.1 11.7 162 19.4 16.8 25.7 38.2 The scatterplot of the data looks like this: Fill in the following table: у X-rank y-rank 1 -0.5 1 2.8 14.4 2 3.7 11.6 3 5.3 20.5 4 7.2 16.2 5 7.8 19.4 6 9.7 16.8 7 11.1 25.7 8 11.7 38.2 9 What is the rank...
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)
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