Consider the vector field Fˆ(x, y, z) = (y/(x^2 +y^2) i - (x/(x^2 +y^2)j (a) compute the curl (b) ) If Fˆ were conservative, what would be the value of the line integral closed integral C(Fˆ · dr ˆ) where C is the unit circle x^2 + y^2 = 1 in the xy-plane? Explain (c) Compute the line integral in part (b) directly (d) From part C, why doesn't it contradict the test for a coservative vector field?

Q: Explain Divergence of curl of B.

A: Let f = f1i+f2j+f3k Then curl(f) is given by ∇×f = ijk∂∂x∂∂y∂∂zf1f2f3=…

Q: Use the cauchy-riemann conditions to determine whether the function f (z) = ((x ^ 3) + x(y ^ 2)) + i…

A: Cauchy-Riemann  : Let f(z)=u(x, y)+iv(x, y) be a complex valued function. Then the Cauchy-Riemann…

Q: Define Vector Line Integral.

A: A line integral is the integral of some function along a curve. One can integrate a scalar-valued…

Q: Solve the conservative vector field by finding the gradient of f(x,y)=(5x^2)+3xy+(y^2)

A: Given: f(x, y)=5x2+3xy+y2 To find: Gradient(or conservative) vector field of given scalar valued…

Q: Q1: Find the derivative of f(x,y,z)=x^2+xy^3-z at point P_o (1,1,0) in the direction of vector V…

A:

Q: Let F = (x^2 + y^2, x^2 + y^2) be a vector field and C be the simple closed curve given by circles…

A:

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

A:

Q: Determine if the surface x^2 + y^2 +z^2 = 1 is tangent to the surface x^2 + y^2 + z^4 = 1 at…

A:

Q: the normal line of the surface [z = (4x^2 + y^2] at the point (1,1,5) O 8x-2y+z=5 O 8x+2y+z=5…

A: We have to find the normal line of the surface.

Q: Given the general vector A=(sin20) a_ find the curl of A at (2,π/4,0) O-0.5a_z 0.5 a_ - a_p 2a_z

A:

Q: Let f(x, y) = x^2/(x + y). Find a unit vector u such that Duf(1, 2) = 0

A: f(x, y) = x^2/(x + y)

Q: Find one normal vector of the tangent plane to f(x, y) = cos(x² +y²) at point P(1,1, cos 2).

A: As we know the expression of the normal vector to the tangent plane at a point on the curve can be…

Q: b) Find the unit tangent vector of 7(t) = (t? – 1)î + t²j at t = 2.

A: We have to find the unit tangent vector.

Q: find    (a)    div(f)   (b)    curl(f) if f=x^2(vector i)+y^2(vector j+2yz(vector k)

A: Let's understand the mathematics behind the div and the curl functions. Please see the expressions…

Q: an object is moving in 3-dimensional space with velocity vector v(t)=(sin(t),t,t^2) starting at…

A: Consider the given velocity vector: vt=sint,t,t2 Find the position vector: Integrate velocity vector…

Q: Line segment D runs from (1, -4, 3) to (2, 0, -1). Determine how much work is done by the force…

A:

Q: Let F(x, y) = (e, e-). Determine the integral curves for the vector field.

A: Given vector field F(x,y)=ex, e-xWe need to find the integral curve.

Q: 1)Let F be the vector 1/yi +1/xj let C be the curve xy=4 from P=(1,4) to Q=(4,1) 2) Evaluate…

A:

Q: Verify Green’s Theorem for the vector field F(x, y) = (x^2*y^2 , xy) and the closed curve C…

A:

Q: Sez dz along the line segment from 0 to 1+ in/2.

A:

Q: = 2e"Vi + Ky³j 3. Calculate the outward flux of the vector field F(x, y) across the square bounded…

A: Given the vector field is Fx,y=2exyi+Ky3j across the square bounded by the lines x=±1, y=±1and given…

Q: 2. Let x'= [5, 1, 3] and y' =[-1, 3, 1]. (a) Find the inner product, y'x. (b) Find x- - 2y. (c) Find…

A:

Q: Q1: Find the derivative of f(x,y,z)=x^2+yx^2-3z at point P_o (1,1,0) in the direction of vector V…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…