Find the Curl of the vector field. F(x,y, z) = 7e" sin(yi+ 8e* cos(y j+ 14z k a. &e" cos(y) +7e" cos(y)]k Ob (8e" cos(y)) k COS Oc (et" cos(y)– 7e" cos(»)) * -(4)sa + 7e* sin y)]k C. COS k Od. "(se" sin(y) O e No correct answer

Q: (1) Is the vector field F(x, y) = (2æ*y^ + æ) î + (2a*y³ + y) Î conservative? Support your answer…

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Match the D.E. with a direction field: y' = t+y – 1, , y' = sin(t)sin(y), , y' = 2 – y, , y' = t(2 –…

A: NOTE: Horizontal axis is t-axis  .

Q: 20) For each vector field F, evaluate the circulation along the curve C consisting of the portion of…

A: Step 1:Step 2:Step 3:Step 4:

Q: In problems 11 and 12, do the computation two ways: i) by using the definition of either flux of a…

A: Using i) the definition of the flux across the surface is  ∬SF.dS.

Q: For each of the following, compute the line integral S. F dr Where Cis a curve with…

A:

Q: If/Given that → F(t)=(5t+3,3t²,8-4t³), Find: - a) The first derivative: b) The first derivative: c)…

A:

Q: Find the curl of the vector field F. F(x, y, x) = 2yz'i + 3xj +&xk O 15r4 O 15:3 O (8yz – 8]j +…

A:

Q: Match each of the functions (a)-(c) with the corresponding gradient vector field from those in…

A: We have to match the gradient vector field

Q: 2. Let z= x²sin2y дz Compute (a) дх (b) дz ду

A:

Q: Let h be a differentiable function of x obtained from the parametric equations a = f(t), y= g(t) .…

A: if x=f(t) and y=g(t) thendydx=dydtdxdt

Q: 6. Consider the system x' = 2r y=-y. I (a) Sketch the vector field. (b) Show that for every solution…

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Q: Find the work done by the force field F(x, y) = 2xy³i+ 4x²y² in moving a particle counterclockwise…

A: The work done of a force F→ along a curve r→ is defined by ∫CF→⋅dr→.Since curve is closed in…

Q: WHICH ANSWER IS CORRECT? Given the curve C parametrized by the vector equation r⃗…

A: Given :- The curve C parametrized by the vector equation r t = 3 sin t i^ +2 - sin t +cos t  j^…

Q: 1-2 Find the domain of the vector function. 1. r(t) = (10(1 In(t + 1), t - 2:21

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Q: (Calculus) The tangent vector to (x(t), y(t)) is (x'(t), y'(t)). The tangent vector's length ||(x',…

A: Given that the tangent vector to and is the speed of the point along the curve at time t .Here also…

Q: Suppose F(x, y) = −y sin(x)i + cos(x)}. (a) Find a vector parametric equation for the parabola y =…

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Q: Show that Sa fdx + gdy = Sa - (16x*y²dx + 8yxʻdy) is independent of path: (10,5) –2) (10,5) ,-2) 4…

A: We are given a line integral as follows : ∫1, -210, 5 fdx+gdy=∫1, -210, 5 -(16x3y2dx+8yx4dy)   First…

Q: Suppose C is the curve from (0, 0) to (2, 0) to (2, 3) to (0, 3) to (0, 0). Find the work done by…

A: