Using Taylor’s Theorem In Exercises 45-50, use Taylor’s Theorem to obtain an upper bound for the error of the approximation. Then calculate the exact value of the error.
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Chapter 9 Solutions
Calculus (MindTap Course List)
- f(x) = {x, 0<x<pi} {2x-x, pi<x<2x}Determine the fourier series for the function definedarrow_forwardwhat is the fourier series of f(t)=e^abs(t) -pi<t<piarrow_forwardSolve the initial value problem using Laplace Transform Solve the initial value problem using Laplace Transform Solve the initial value problem using Laplace Transformarrow_forward
- finding the 3rd harmonic of the Fourier series.arrow_forwardSolve the Fourier series of f(x) = (a+b)x -π < x < πwhere a and b are the first and second digit of your roll number respectively roll no is 070arrow_forwardLinear Algebra Find the second-order Fourier approximation of the function f(x)= x on −pi less or equal to x less or equal to pi.arrow_forward
- Find the Fourier series (ao, an, bn and the fourier series formula f(t) = 8 − t3 − 8 < t < 8arrow_forwardUsing the Heine-Borel Theoremarrow_forwardThe Fourier series representation, FS(t)FS(t), of a function f(t)f(t), where f(t+4)=f(t)f(t+4)=f(t) is given by FS(t)=a0/2+∞∑n=1an cos(nπt2)+bnsin(nπt/2) In this particular case the Fourier series coeffcients are given by a0=0.75a0=0.75 an=6(−1)n/nπ bn=2(1−2(−1)n)/n2π2 Compute the Fourier series coefficients for n=1,2,3n=1,2,3 correct to 4 decimal places and hence, using these entered values, compute FS3(3)FS3(3) correct to 3 decimal places. Enter the values in the boxes below. Enter a1 correct to 4 decimal places: Enter a2 correct to 4 decimal places: Enter a3 correct to 4 decimal places: Enter b1 correct to 4 decimal places: Enter b2 correct to 4 decimal places: Enter b3 correct to 4 decimal places: Enter FS3(3)) correct to 3 decimal places:arrow_forward
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