Activity 2 Given these dataxy0.51.31.31.83.22.24.02.56.32.8Calculate 2.5) using Newton's interpolating polynomials of order 1 through 3. i.e. a) f₁(x),b) f₂(x), and c) f3 (x)

Firstly, set up the forward divided difference table for the given data. x f(x) Ist diff…

Answered: Activity 2 Given these data 0.5 1.3 x y…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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a) Use Newton interpolation to find the unique cubic polynomial f that passes through the points (0, 1), (1, 1), (2, 1), (3, 4). If we write f as a linear combination of binomial polynomials f(x) = E a, (:), what is the coefficient a2? %3D O 1 O -2 O -3
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3 FEBIT-MATHEMATICS 2-ASS1-2 Use the following information for Questions 10 and 11: 2ty =Y+4. t 10.The derivative of the left-hand side of the equation with respect to t is: 11.The derivative of the right-hand side of the equation with respect to t is: 12. The second-degree Maclaurin polynomial for f(x)= vx+9 is 3+ x2 If this 6 108 polynomial is used to approximate v8, the answer is: dy 2- 3t 3+2t is 1+t 13. of the parametric equations x = and y dx 1+t Use the following information for Questions 14 and 15:
ra+t If f(z) = f(a + 1), then prove that the value of f(z)dr is independent of a.
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Where does the function f(x) = x – x %3D have an inverse? O a. (- O b. [0, 00] Oc. 0, 1) O d. [-1, 1] O e. ((-\infty,0) \cup (1, \infty) \) O f. (-\linfty, \infty) \)
Use R functions to conduct the following 1. Calculate the following quantities: i) the sum of 80.3, 34.9 and 112.01 ii) The square root of 121 iii) 10-based logarithm of 1000, and multiply the result with the sin of 2n 2. Use the function cumsum() to calculate the cumulative sumation of the elements of the vector v = (2.3, 5.7, 1*10-7, e) 3. Calculate the cumulative sum of the previous numbers in reverse order. Hint: use the rev function 4. Assigns numbers 10 and 20 to varaibles s x and y, then write R commands for the following i) store the result of multiplying x and y in a new variable z. ii) Creat a vector My Vec of the objects x, y and z. iii) Find the minimum, maximum, length, and variance of MyVec 5. The follwing numbers are the error in measurment in an expriemnt 0.1 0.6 33.8 1.9 9.6 4.3 33.7 0.3 0.0 0.1, store them into a vector MesErr. 1) What is the mean and the standard deviation of the errores ii) which item has maximum error ii) calculate the cost of correcting the error…
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providing the function down below, at the points ?0 = 0, ?1 = 1 and ?2 = 2. Write the Lagrange and Newton interpolation polynomials for 3 points, and compare.
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Interpolate the following data set with Newton interpolation (P(z) = b, + b (z - 11) + b2(z - z1)(z – 2) + ba(z – I1)(z - z2)(z – z3) 1.0 12.0 13.0 14.0 Yi 1-5.6|-9.4|-23.2|-65 The coefficient b, is Answer: The coefficient bị is equal to Answer: The coefficient b, is equal to Answer: The coefficient by is equal to Answer:

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Activity 2 Given these data 0.5 1.3 x y 1.3 1.8 3.2 2.2 4.0 2.5 6.3 2.8 Calculate 2.5) using Newton's interpolating polynomials of order 1 through 3. i.e. a) f₁(x), b) f₂(x), and c) f3(x)