4. An interpolating polynomial of degree 20 is to be used to approximate e-² on the interval [0,2]. How accurate will it be? (Use 21 uniform nodes, including the endpoints of the interval.)

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A: We use definition of eigenvalue and corresponding eigenvector of matrix A.

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A: (a) For every m ∈ Z, 5 | (m2 −m2) = 0      Hence, m ~ m for all m ∈ Z      Hence, ~ is reflexive.

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Q: 3. Given the data 01 6 f(z)|19|23|93 259 construct the divided-difference table, and compute an…

A: NETWON DIVIDE DIFFERENCE TABLE IS GIVEN AS-:

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Q: Theorem 1.5. The principal normals at consecutive points of a curve do not intersect unless ↑ = 0)

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A: USE THE VALUES  -1≤y≤1 and y2-1≤x≤1-y2  just put them in given integral,we get…

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A: Given the equation,                   sin(3x)=-0.172.

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A: We are given the differential equation      3y" - y' - 2y = 100cos(2x)  Differentiating w.r.t x…

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A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Two zeros of P(x) = 5x2(x7 − 14x + 3) are 0. How many other zeros are there?

A: The given polynomial is P(x)=5x2(x7-14x+3) Number of Zeroes The number of zeroes of a polynomial is…

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Q: u(c) = − +2sinh + 1.² ( (x - t)u(t)dt

A: Given: The Volterra Integral Equation is given by:                          ux=-x+ 2 sinhx+∫0xx-t ut…

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Q: 8. Let S be the surface r(u, v) = integral F. ds where F(x, y, z) S (tan v, u sin v, u²) where 0 ≤ u…

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A: Let W=0. The integral becomes I0=∫Cz3+2z+1z-0dz. Now 0 is the singularity of the integrant. So let…

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Q: subject to: Max z 4x12x2 + x3 2x1 x3 = 5 x2 + 3x3 3x1 + x₂ ≤ 6 X1, X2, X3 20 - -7

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