For Exercises 1-4, use Green's Theorem to evaluate the given line integral around the curve C, traversed counterclockwise. 3. 2y dx-3xd y; C is the circle x² + y² = 1

Q: 3. Use implicit differentiation to find əz - for ?х x²+2y²+5z²=2.

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Q: 2. Write the formula for tangent plane of a function f(x,y) at a point x = a.y=b. How does this…

A: Conisder a function f(x,y).We need to find the tangent plane at x=a,y=b.Let z=f(x,y) and…

Q: Evaluate the line integeral F. di where C is the curve given by 7 (t) = tỉ – t3 + 2tk, 0S t < 2 and…

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Q: Let C be the circle given by x² + y² = 1. Evaluate √(-2x²y + cos x)dx + (2 xy² + y²e³)dy going in…

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Q: where C is the circle with positive orientation. e2021z dz Yo (22 + 4)² (2² – 1) (a) C: |2 – 2 – i|…

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Q: SHOW COMPLETE SOLUTION, MAKE THE SOLUTION CLEAR. THANK YOU!

A: Step 1: Step 2: Step 3: Step 4:

Q: Let C₁ be the straight line from the point (1,0) to the point (0,1) in Figure 1. Let C₂ be an…

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Q: Evaluate f (5ydy + 3xydx) C if C is the closed curve determined by the x-axis, the parabola y = x²…

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Q: Evaluate  ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9  with positive…

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Q: Let C be the curve consisting of line segments from (0, 0) to (1, 1) to (0, 1) and back to (0, 0).…

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Q: Let F(x, y) == and let C be the circle r (t) = (cost)i + (sint)j, 0 ≤ t≤ 2π. A. Compute მი Note:…

A: Step 1: Step 2: Step 3: Step 4:

Q: Consider f (x, y) 3x² + xy + 3y². Use calculus to find the extreme values of fon the circle x² + y²…

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Q: 1. Let F = (vi-x)/(x² + y²), evaluate § ♬ dr, where C is circle (x − 1)² + (y − 1)² = r² with 0 <r…

A: We are given that          F = (y i - x j)/(x2 + y2)   Now, r = x i + y j       =&gt; dr = dx i + dy…

Q: (c) Find all curves y: R → R² such that y(t) = y(t) and y(0) = (1, 2)

A: Cur