Let C be the positively oriented square with vertices (0,0), (1, 0), (1, 1), (0, 1). Use Green's Theorem to evaluate the line integral l 10y²x dx + 8x²y dy. C

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Q: 1. P 2. P→Q 3. ¬QVR :.R 4. Q 5. Q 6. R 2,1 4 3,4

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A: Consider the given cyclic group, Z3x/x3+2x+2* It can be observe that x3+2x+2 has no zero in Z3. So,…

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A: (a) ∑n=0∞-1ncosn3n-2 it is known that a series ∑nan is absolutely convergent if ∑nan is convergent…

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A: The details are given in step 2.

Q: (c) Give one example where the Green theorem fails, and explain how.

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Q: Using the given data set, determine the interpolated value for x = 19 Use Lagrange Method

A: Given the data set, x 5 9 11 14 17 20 24 26 29 33 y 86 -49 -37 -27 -83 24 57 54 65 46 and…

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A: Explanation of the answer is as follows

Q: Suppose K is an extension of F of degree n. Prove that K can bewritten in the form F(x1, x2, . . . ,…

A: Suppose K is an extension of F of degree n. To Prove: that K can be written in the form F(x1, x2, .…

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Q: Define the set G= ={[ 0]|PER} cos sin 0 - sin cos (a) It is a fact that G is a group. You do not…

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Q: Using the given data set, determine the interpolated value for x = 33 Use Lagrange Method X y 5 -36…

A: x 5 8 11 14 17 20 24 27 30 33 y -36 -49 -96 44 45 37 -26 -46 62 11 Lagrange's Interpolating…

Q: Use one of the equiv statements to conclude that the matrix below is not a positive definite matrix.…

A: Given : B=123204341 To Explain : B is Not positive definite

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Q: A) Consider the vector field F(x, y, z) = (-3yz, 6xz, xy). Find the divergence and curl of F. 0…

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Q: T = (p² x go!!). po!!! ||r² × p/ || 2

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Q: Consider the statement: If n is a cube of an number. integer, then n is a square

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Q: I. Let F = 8xi +8yj + 10zk. Compute the divergence and the curl. A. div F = B. curl F = II. Let F =…

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A: Graph of the function is given. We have to find its equation.

Q: -. Determine the values of a for which the system x + 2y3z = 4 3x = y + 5z = 2 4x + y + (a²-14)z = a…

A: The given system is ,            x+2y -3 z= 43x-y+5z   = 24x+y+a2-14z=a+2 rewrite the given system…

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Q: S1. Assume 6² - 4ac <0 in ar²+bx+c, what is the imaginary part of the root?

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Q: 1-2 Classify each function as a power function, root function, polynomial (state its degree),…

A: According to our guidelines we can answer only three sub-parts and rest can be reposted.

Q: 1. Let 3 be the permutation α, β € Σ3 such that Here a² = aa. group of {1,2,3}. Find two…

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A: Use definition of disconnectedness mentioned below.

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A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 3 Find the curvature X of the plane curve y = x + = at x = 3. x K=

A: According to our guidelines, we can answer only the first question. Kindly repost the other…

Q: Let CE Rxn be a matrix such that xCx>0 for all nonzero vectors x ER". Prove that C is nonsingular.

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