Compute Div(F) and Curl(F): F--(4y-1) i+yj+(-3y) k

Q: Findtheintersectionof2x+2y+z=4andx+2y+3z

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Q: Let R = {(x,y): |x| + |y| ≤ 2}. Use the transformation x=u+v, y=u-v to evaluate ∫∫ ((x^2)*(e^y))dA

A: Consider the given: R=x,y:x+y≤2x=u+vy=u−vA=111−1=−1−1=−2=2

Q: Calculate grad div F+ curl F at P(-1, 1, 1) where − = (3xz²)i + (xy)j + (2yz)k. O 7i+ 4j - 3k D-3i -…

A: we will find the required.

Q: Determine the interpolating polynomial in Newton's form that passes through the points and Use the…

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Q: Find a polynomial y = p(x) of degree 4 that goes through the points (0, 4), (1, 2), (2, -4), (3,…

A: solution of the given question is like this:

Q: Given the rule (x,y) --> (x-4, y+8), describe what transformation occurs to any given point

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Q: [61] Diagonalize B = (by finding P and D) or explain why B isn't diagonalizable.

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Q: find the quadratic polynomial whose zeores are (I) 3,-4 (ii) 2,1

A: Given problem is : find the quadratic polynomial whose zeroes are (I) 3,-4 (ii) 2,1

Q: Using Newton's Divided Difference, the interpolating polynomial of the points (xo.Yo) = (- 2,1),…

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Q: Let P0. (x) denote the quadratic polynomial that interpolates the data {(xo, yo), (x1, y1), (x2,…

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Q: calculate div(F) and curl(F). F = (xy, yz, y² – x³)

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Q: Compute the curl of F = (2xy, x²y + x²).

A: Here we have to find the curl of the given vector field F.

Q: Does (Z11 , + , .) have subfields? In this case which subfields.

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Q: under the linear transformation T: R² → R² consisting of a reflection in the y-axis followed by a…

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Q: Write x3 + 2x + 1 as a product of linear polynomials over some extension field of Z3.

A: Given: x3+2x+1. To Do:We have to write x3+2x+1 as a product of linear polynomials over some…

Q: Calculate the 1st order Newton polynomial that interpolates the two data points (1,1),(2,3). Now…

A: We can use Newton's forward difference interpolation method to find Newton's polynomial.

Q: Show that V² (v-x) = 2V.v+x-V²v, where v is a vector field and x is the position vector of a point…

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Q: EXAMPLE 1 Using the Strategy Find two numbers whose sum is 20 and whose product is as large as…

A: Given sum of two numbers be 20

Q: Find curl(zi + xj+ yk).

A: Using definition of curl of vector.

Q: If F = ⟨F1, F2, F3⟩ what is div (curl(F))

A: F = ⟨F1, F2, F3⟩

Q: Find a quadratic polynomial whose zeroes are (i)3, -4 (i)2, 1

A: Quadratic  equation = x2-(Sum of zeroes)x + product of zeroes =0

Q: 3) Compute the curl of F= (4xy) i + (2x² + 2z²³)j + (4 yz) k.

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Q: Using Newton's Divided Difference, the interpolating polynomial of the points (xo.Yo) = (- 2,1),…

A: We use Newton's Divided Difference interpolation formula. x      x0      x1      x2      x3y      y0…