a) Calculate f(3.4) using Newton's interpolating polynomials of order 1, 2 and 3. All numeric values shall be expressed with 4 decimal places.

Q: Find the interpolating polynomial of the following points or functions using Newton's

A: Given: The points -2, 2, -1, -2, 1, 3 and 3, -3. To find: Interpolating polynomial.

Q: Find the Newton's polynomial which interpolating the following data. 1 2 3 4 5 f(x) 3.6 1.8 1.2 0.9…

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Q: Make up two functions  f1and f2 that have the same Laplace transform.

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Q: Approximate f' (2) using the given data f(0) = 2, f(1) = 3, f(2) = 12, and f(3) = 41 and the…

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Q: Find an expression for the nth Maclaurin polynomial using sigma nota- tion for the function cosh x.

A: Suppose f has n derivatives at x=0 then nth Maclaurin polynomial of f is pn(x) where pn(x)=∑k=0n…

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A: The Maclaurin series; fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+.... Where the center is at x=a=0…

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A: The Legendre polynomials are as follows.…

Q: Consider the following table: Xi 5 6 f(X) 7 12 14 Find f(4) using Lagrange method for interpolation.…

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Q: Write down the trigonometric Fourier series representation of the following signal: x(1),

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Q: From the given data, identify f(4) using Newton's polynomial. (2,10), (3,15), (5,25), (8,40)

A: Explanation of the solution is given below....

Q: (a) Find the equation of the following curve Ax) using Newton's divided difference polynomial.…

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Q: find the fourier transform of the function St)= -at 2.

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Q: :Q4: Use the Fourier Transform properties to find the FT of the following signals (a) x1(t) = x(1 –…

A: Only 1st individual question is to be answered.

Q: Q2. Consider Xi 0.12 yi 0.7917 0.7733 0.7437 0.24 0.36 0.48 0.7041 0.6563 0.6023 0.60 0.72 Using…

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Q: For a given data (x,f(x)):(-1.89,-4.179169),(0,-1),( 1.89,9.323369), estimate the function value at…

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Q: Obtain the Fourier expansin f I+ 9X în -3 LXLO 3 f(x) = %3D 3.

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Q: Calculate the Tayorl Polynomials T2(x )and T3(x) centered at x=a for f(x) = 14 sinx, a=pi/2

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Q: Approximate f' (2) using the given data f(0) = 2, f(1) = 3, f(2) = 12, and f(3) = 41 and the…

A: The given data is f(0)=2 ,f(1)=3, f(2)=12, f(3)=41.

Q: What is the Fourier transform of the following e-j10ntx(t)

A: The Fourier transform of the function f(t) is represented as F(k), it is defined as ∫-∞∞e-jktf(t)dt,…

Q: find directly the Laplace trans- forms of the functions described (by formula or graph) in Prob-…

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Q: Use the fourth Maclaurin polynomial for cos(x) to approximate cos(-). Round your answer to 11 four…

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Q: (a) Develop a table of f(x)=2e* + 3x for x = 3, 5, 7 and 9. (b) Estimate f(4.2) using the…

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Q: Given the data: 2.1 2 1.4 2.7 3.4 3.2 y 12 8. 2 5. 10 17 Determine y at x= 2.5 using: a) Newton's…

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Q: The Maclaurin expansion of f(x) = sin (3x) is

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Q: What is the laplace inverse of 5 -3s -7s - S

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Q: Fit a second order Newton's interpolating polynomial to estimate log 10 a) Interpolate using xo =…

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Q: Find the max and min values on the given interval for #3 and x+5 3. у %3 [-3,3] 16-x2 T- 4. у %3D…

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Q: what is the approximate value at point x- 0.7 of the interpolation polynomial obtained using the…

A: We have the following values: x y -1 4 0 11 1 16 2 13 Now, let make the backward…

Q: Approximate f' (2) using the given data f(0) = 2, f(1) = 3, f(2) = 12, and f(3) = 41 and the…

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Q: (b) What is the Fourier Transform of x?8(x² – a²)?

A: The given problem is to find the Fourier transform of the given function, in the given function…

Q: Approximate f' (2) using the given data f(0) = 2, f(1) = 3, f(2) = 12, and f(5) = 147 and the…

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Q: Fit a second order Newton's interpolating polynomial to estimate log 10 a) Interpolate using x, = 8,…

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Q: Construct Newton's forward and Backward Difference polynomials to approximate the following function…

A: To obtain the interpolating polynomials, use the following formulae. Newton's forward difference…

Q: 2.Use the Newton interpolation polynomial to find f(0.05) based on the following data points {(-0,5,…

A: Given data is  {(-0.5,0.97939),(0.15,4.72743),(0.5,13.69506),(1,61.25661)} we have to find the value…

Q: a) Develop a table of f(x)= e¯* + 5x for x = 2, 4, 5 and 8. b) Estimate f(3.2) using the…

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Q: Derive the following Fourier transform: cos (2Nfot +0) ½ [8 (f + fo)e® + & (f - fo)e® ]

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Q: Consider the following data set x |1 12 13 y18.2|22146.2 Interpolate this data set using Newton…

A: The value of the table for x and y x 1 2 3 y 8.2 22 46.2 We have to interpolate this data…

Q: 2. Consider the data: X 0.1 0.2 0.3 0.4 0.5 f(x) | 1.40 1.56 1.76 2.00 2.28 Use the Newton's forward…

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Q: Find the Fourier expansion for the function intersad -ist <I fit) : t-t in the

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Q: Find the Lagrange and the Newton forms of the interpolating polynomial for these data: -2 0 1 f(x) 1…

A: Given data : x   -2   0  1 f(x)    0   1  -1 Lagrange Interpolation formula: Let…

Q: Calculate f (3.4) using Newton.s interpolating polynomials of order 1 through 3 and estimate the…

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Q: Approximate f' (1) using the given data f(0) = 1, f(1) = 2, f(2) = 1, and f(3) = 10 and the Lagrange…

A: Lagrange inteerpolation is used to find a polynomial equation which passes through the given set of…

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Q: Given these data, calculate f(2.8) using Newton’s divided-difference interpolating polynomial of…

A: We know that nth order polynomial of Newton's interpolating polynomial is defined as below,…

Q: Given a set of data points determine Newton's interpolation polynomial of higher degree which passes…

A: The given points are: x -1 0 1 2 fx 3 -4 5 -6   We have to find Newton's interpolation…

Q: Use Newton.s interpolating polynomial to determine y at x= 8 to the best possible accuracy. 1 2 5.5…

A: Given data is  To find the value of y at x=8 using Newton's interpolation formula,

Q: Compute the coefficient Fourier a, of the { T - r, 0<r<* 0, f(r) =

A: We have to compute Fourier coefficient an.

Q: Given that f (x) = x+x for - T<x< T, find the Fourier expression of f (x). Deduce that 1 1 = I+ + 32…

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Q: Give the Fourier Transform for the following functions (ii) 10 + 4cos5t

A: The Fourier transform of the function f(t) is represented as F(k), it is defined as…