Find the Taylor polynomial T3(x) for sin(2x) centered at 0. What is T3(1)? (T3 is suppose to look

Q: y = exp( 2-x ) at x = [-1,2].

A: Given   y=e(2-x) , in the interval x=-1,2 So the value of y at x=-1,0,1,2 are…

Q: Let f(x) = sin x. Find a polynomial P(x) of degree at most 2 such that P(1) = f(1), P(1.1) = f(1.1),…

A: So we have to do a lagrange interpolation to approximate the function f(x) = sin(x) about the…

Q: find the residue at each pole of the function 1 f(z) = (2² - 2x + 2)² 2z

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Q: the error estimate for Taylor polyno

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Q: Determine the pole of the functions and residue at each pole for f(z) =Z2-2z (2²+4) (z+1)²

A: Step 1: Given the function f(z)=((z2+4)(z+1)2)(z2−2z)​ =>f(z)=(z+1)2)(z2+4)(z2−2z)​…

Q: Calculate L6 for f(x) = √6x + 3 over [1,3].

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Q: LOW: Construct polynomia -) sinx in [0, 2π] interpolation in mentioned interval of the function

A: Thank you for the question. According to our guidelines we can answer only  first question and…

Q: 5. Find the asymptotic behavior of the polynomial f(x) = -x"+4æ® + 2x³ – x³ + 10x? – 12x – 10 (i.e.…

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Q: 2. Find the Maclaurin polynomials of order n=0,1,2 for f(x) = cos(x).

A: Consider the formula for Maclaurin series: Calculate the derivatives to find the terms in the…

Q: 1. Using the points xo = 1 , x1 = 1.6, and x2 = 2.5, find the Lagrange interpolating polynomial that…

A: We find the Lagrange interpreting polynomial using the given points and that fits the function 2/x2.

Q: Consider the Lagrange polynomial that passes through the 4 data points given by 2 8 y 7 | 151 | 407…

A: We know that L0x is given by  L0x=x-x1x-x2x-x3x0-x1x0-x2x0-x3        1 Here, x0=2,x1=5,x2=7,x3=8,x=4…

Q: 4) Calculate lim (√t-3, V-2, tan t-4 t-4 (-)). HINT: On the second component, you can factor t - 4…

A: To find:-

Q: Find the residue of the following functions: z3 i. f(z) : at z = 1,2,3. (z-1)(z-2)(z-3) 1 2 ii. f(z)…

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Q: nich of the following is a polynomial function? a. y = sin x b. y = cos x C. y = 3x d. y = x³

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Q: 4. Explain how the following formula d (u₁-u₂-..- U₂) ² dx enable us to differentiate any…

A: The given formula is:ddxu1-u2-...-un=du1dx-du2dx-...-dundx. To Do:We have to explain how this…

Q: The error will disappear when using f(x)=x* to find the Lagrange interpolating polynomial p(x) if n…

A: Sol

Q: (b) Construct the Lagrange polynomial. y=sir interpolation. the for function y=sinak taking points…

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Q: Find the formula for the fourth degree polynomial containing the point (0,8) and whose graph is…

A: We have to find the equation for the given graph.

Q: Generate eight equally spaced points from the function f (t) = sin?(t) from t = 0 to 2n. Fit this…

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Q: 2. If m < n, show that mPa(x)dr deduce that r* P6(r)dr = 0. = 0, where Pn(x) denotes the Legendre…

A: We have prove the given problem.

Q: Find Ao, A1, A2, and A3 in rewriting the function of f(x)=- x20 in terms of Lagure polynomial, x<0…

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Q: When calculating the first Lagrange polynomial using xo, X1 we obtain L,(x) = x – 3, then xo and x1…

A: Lagrange's polynomial can be used to obtain the interpolation for the data. The polynomial is…

Q: 3. Find a second-degree polynomial P such that P(2)=9, P'(-1)=-13 and P"(5)=6.

A: We have to a second digree polynomial, which satisfies the given conditions. Standard form of a…

Q: consider the polynomial f (x) = 7x4- (2 + 2x + 6x2 + 5x3) -8x5. In x = 0.7, use the approximation…

A: Given the polynomial fx=7x4-2+2x+6x2+5x3-8x5 and x=0.7 and ∆x=0.2

Q: Find the residue f(z) = Z²-22 (2+1)² (2²44)

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Q: 3. Is the polynomial f(x) = 2x° + 30r – 150 € Q(r] reducible or irreducible over Q? In either case,…

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Q: 4. Find the remainder of f (x) = (1 + x)3/² of degree 3.

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Q: find the differentiate of h(t)= the 5th square root of t - 5e to the power of t

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Q: Consider the following quadratic f(x) = x - 14x +4 with the roots a and B. Suppose the new quadratic…

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Q: 3. Plot the function x+1 f(r) = 1+ 12r² * in the interval -1 SIS 1. Then fit a line (o = co + Cir)…

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Q: Find a second degree polynomial P such that P(2) = 7, P'(2)=5, and P"(2) = 2.

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