Use Stokes' Theorem to find the value of the line integral of the vector field Faround the curve Cwhere C is in the direction of positive orientation (that is, counterclockwise when looking down from the positive z-axis): f. v - dr - [[ (cart 1) F. = (curl F). n ds where F(x, y, z) = xyi + x²j + z²k and Cis the intersection of the paraboloid z = x² + y² and the plane z = y.

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Q: Residue of

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Q: Example 8: Approximating Sums n Find the approximating sum f(c)Ax, for the function f(x) = 2x+5 on…

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Q: 6. Consider the system: | | dt = 2.r y(8 + 2y) + 2ry

A: Given: Let us consider the given system, dxdt=14xy-2x⇒Fdydt=y8+2y+2xy⇒g

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Q: A penny collection contains twelve 1967 pennies, seven 1968 pennies, and eleven 1971 pennies. If you…

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Q: Let fn be the n-th Fibonacci number of Example 3c in 8.1, k=n k=n An = Σκ=1+2+...+n, Bnk²= 1²…

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Q: Let R be the relation on a set {1,2,3,4,5} containing ordered pairs (1,1),…

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Q: Q2):- Find Y[Z] of signal Y[n] (Cos wn). U[n]

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Q: Let fn be the n-th Fibonacci number of Example 3c in 8.1, k=n k=n = An Σ=1+2+. .+ n₂ =k²= 1² +2²+.…

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Q: ential equati x²y dy = C

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Q: From a numerical perspective integration is better conditioned than differentiation.

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Q: Evaluate f C F = (x² +

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Q: f5 4 18-21. The production function for making widgets is P(x, y) = 4,600x3/8y5/8 Where p is the…

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Q: (a) Use differentiation to find a power series representation for 1 F(x) = (4 + x)² 00 f(x) = = Σ…

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Q: L {sin(wt + O)}; w and O are constants

A: The solution is given as

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Q: Problem 3 Given: Arg(Ln(z)) = 3 (radians) and |2| = 70. Find S = Im(z) + Re(z)

A: The solution is given below