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

Q: press the improper rational transform: 3 4 X(z) = 1+ + + 1 3 ms of a polynomial and a proper…

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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: 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: Let f: (-pi/2 , pi/2) -->R be given with f(t) = tan-1(t) What is taylors polynomial P1(t)  of the…

A: f(t)=tan-1(t),  f(0)=tan-1(0)=0first we find the derivative of f(t) f'(t)=11+t2f'(0)=11+0=1taylor…

Q: For the following, find the Maclaurin polynomial of degree n. (a) xe", where n = 3 (b) vsin(x),…

A: The answer is given below:

Q: 4. a) Find the second Taylor's polynomial P2(x) approximating the function f (x) = e2* + cosx about…

A: Given function is fx=e2x+cosx.

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: Find the interpolating polynomial of degree two for f(x) cos(r2) +r on the interval [-1, 1] using…

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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: 3. Determine the pole and the residue of 22+1 f(x) 24-z-2

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

A: Sol

Q: Find the 5th order Taylor polynomial about a = r for sin x.

A: To find Taylor polynomial for given function

Q: approximate the value of cos (1/2) (sixth degree Maclaurin polynomial)

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Q: Verify that the Legendre polynomial Pn(x) satisfiesthe second-order equation(1 − x2)y'' − 2xy' + n(n…

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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: Find the Taylor polynomial T(x) for sin(2x) centered at 0. What is T(1)?

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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: 13. Find the transformations present in g(x) = (1/2)((-3/4)x – 21/4)2-4 compared to f(x) = x2. Use…

A: Concept - shift the graph as many as necessary in up ,down ,left and right

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: 12. Let f(a) be a function with f(1) = 2, f'(1) = 6, f"(1) = -12. Which of the following is the…

A: according to bartleby guide line we do only first part of multiple 12)  given  f(1)=2  , f'(1)=6,…

Q: 2. (а) Find the function P(x) = a +b cos(n x) +c sin(nx), which interpolates the data 0.5 1 y 4 (b)…

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Q: What is the degree 3 Taylor Polynomial for sin x for a near T 지/2?

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Q: Construct the Langvange inter po lation polynomial for the function y= Sin Tx, taking the points %3D…

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

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