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Mathematical Methods in the Physical Sciences
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- 5. Use appropriate Lagrange interpolating polynomials of degrees one, two, and three to approximate each of the following: f (8.4) if f(8.1) = 16.94410, f(8.3) = 17.56492, f (8.6) = 18.50515, f (8.7) = 18.82091 b. f (-) if f(-0.75) = -0.07181250, f(-0.5) = -0.02475000, f(-0.25) = 0.33493750, f (0) = 1.10100000 f (0.25) if f(0.1) а. = 0.62049958, f(0.2) = -0.28398668, f(0.3) = 0.00660095, f(0.4) = с. 0.24842440 d. f (0.9) if f(0.6) = -0.17694460, f(0.7) = 0.01375227, f(0.8) = 0.22363362, f(1.0) = 0.65809197 7. The data for Exercise 5 were generated using the following functions. Use the error formula to find a bound for the error, and compare the bound to the actual error for the cases n = 1 and n 2. f(x) = x In x f (x) = x + 4.001lx? + 4.002r + 1.101 f(x) = x cos x - 2r2 +3x - 1 а. b. с. d. f(x) = sin(e - 2)arrow_forward11. a. For the function f(x) = (3x+2), let x, =-1, x, =0, x, =1. Construct interpolating polynomial to approximate f(0.5). b. Find an error bound for this approximation.arrow_forwardA) - 4. Consider the functions g(x) and . Determine (13)- (),SA [ 5A] 2arrow_forward
- Q2. Consider Xi yi 0.7917 0.12 0.24 0.7733 0.36 0.7437 0.48 0.7041 0.60 0.6563 0.72 0.6023 Using Newton's interpolating polynomials of order а) 1 b) 2 c) 3 to estimate the function for x = 0.40.arrow_forwardAre the following two polynomials orthogonal to one another between 0arrow_forward4. Find a formula for [₁ f(x) dx 1 in terms of the functional values f(x₁) and ƒ(x2), which is exact for linear polynomials. For what values of x₁ or x2 is the discretization formula super- accurate, that is the truncation error is of higher order than expected? What kind of discretization does this correspond to (Forward, Backward, Center etc.)?arrow_forward8- Calculate M6 for f(x) = = √7x on [0,2]arrow_forwardIf f(x) is known at the following data: xi 0 1 2 3 4 5 fi 1 2 4 8 16 32 Show the Newton’s Forward difference table Determine the equation of the polynomial C. Find f(1.5), f(2.5), and f(4.5)arrow_forward2. Consider the Newton polynomial Pn(x) = ao + ai (x-ro) + a2(x-To)(x-21)+... +an(z-To)(z-I₁). (I-In-1) ... that interpolates f(x) at zo, 21,,Zn. It is easy to see that ao = f[ro]. Show that a1 = f[ro, zi], a2 = f[ro, r1, 12], and a3 = f[ro, 11, 12, 13].arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningIntermediate AlgebraAlgebraISBN:9781285195728Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningElements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,