Evaluate [ F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. Sc C: smooth curve from (-3, 2) to (3, 2) [4(2x + 3y)i + 6(2x + 3y)j] - dr .

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Q: #12- Fnd the indefinite integral of the follaung funchon and check the result by differentionion.

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A: fx, y=-x2y2x2+y2 Now, z0=fa, b=f1, -2=-12-2212+-22=-45 Now partially differentiating fx,…

Q: c) Find the second degree polynomial approximation to f at (a, b) = (1, – 2) T2(x, y)

A: Given :- The second degree polynomial approximation to f at a,b = 1,-2 f x,y = -x2y2x2 +y2

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A: we have given: x=13u+v and y=132u-v  u=x+y, v=2x-y Now, Consider the integrals, ∬R6x+3ydA where, R…

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A: I have provided a graph of this in step2

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A: Step 1: Step 2: Step 3: Step 4:

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Q: 6. Prove that |xy| = |x|ly| for all real numbers x, y.

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Q: Prove where the following complex function is analytic

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