Suppose you need to integrate the vector field v = (3 cos z, e+, sin(y)) along the curve parameterised by r(t) = (t, t, t) from the point (1, 1, 1) to the point (3, 9, 27). %3D Which of the following integrals should give the correct answer? | (3f sin(t) + (1 + 2t)e*+* + 4t° sin(t*)) dt | (3 cos(t) + 2te*+t* + 3t sin(t*)) dt | (3 cos (3t) + 2te2t +3t sin(4t)) dt | (3t sin(3t), 2t(1 + 2t)e*+f", 2t° cos(4t) dt None of these.

Q: Q6: Find the outward flux of the vector field F=(x²y+e'sin(y))i+ (x²+e'cos (y)) j through the right…

A: Given vector field is F=  x2y + ex siny  i + x2 + ex cosy j Curve r2=cos2θ

Q: 4. Find the work done by the force field F (x,y) = (x + y)î + (xy)ĵ in moving a particle along the…

A: The force field is given by F→ = x+yi^+xyj^ The end points of the straight line along which the…

Q: 4. If div F >0 in a region enclosed by a small sphere, the outward flux of the field across the…

A: Given: Divergence F>0 is enclosed by a small sphere in a closed surface . The objective is to…

Q: If a vector field F (x, y, z) = (evz-, In (x² z), sin z), which of the following values is equal to…

A: We have to find div F(-1,0,1).

Q: 19. Find. thedivergen ce. and.cur..4the fellowiny vecter. field: a.. F = Xej+. y.e... b. Ês ĕsiny i…

A: We need to find the divergence and curl of the following vector fields. a. F→=xeyj+yezk=(0,xey,yez)…

Q: Suppose you need to integrate the vector fieldv – (3 cos z, ef sin y)) along the curve parameterised…

A:

Q: Find the outward (normal away from the z-axis) flux of the field F = y2î + xzî – k across the cone z…

A: In this, we find the flux of the given function across the given cone z=3√(x^2+y^2).

Q: Find the solution in the form of Fourier integrals: U4-3uzz = 0, |u(x, t) bounded as x → ±0, sin r…

A: We are given the following second order partial differential equation : ut - 3uxx = 0  ;  -∞ < x…

Q: 2. Find the curl of the vector field. F = z°e* sin(2 y)i – e' cos yj+ xyzk to

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Q: 5. Find the potential function for given vector field: F = (e* In(y))i + + sin(2))j + ycos(z)k

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Q: Find the path of a heat-seeking particle placed at point P on a metal plate with a temperature field…

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Q: Given the upper hemisphere (S) with the equation: S{x² + y² + z² = 81² + 2822 (S): {{x² + y² + z² =…

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Q: Q2: Find the work done S. F.dr in the force field F = yzî + xzĵ + xyk in moving from (1,1,1) to…

A: The equation of a line joining by the points and is given as the following.

Q: The work done in carrying a -1C charge from point A(0,0,0) to the point B(6,0,0) in the field E =…

A: Given,     E=2x.ax^+ 2yay^  VmQ=-1CPoints are A(0, 0, 0)  and  B(6, 0, 0)

Q: Find the conservative vector field for the potential function by finding its gradient. 9 (r,y, 2) =…

A:

Q: Show that the field F = (cos x)i + (- y sin y)j + (z3)k is conservative and Önd a potential function…

A: F = ( Cosx )i + ( -y Siny )j + ( z3 )k  F = gradient ( - Sinx - y Siny - Cosy + z4/4 ). Thus, we can…

Q: Evaluate line integral of vector field F(z,9) = i+ 1- x? y2 2x along the curve x = cos(t), y =…

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Q: | 23. Find the outward flux of the field F = ( 3xy i + (e* + tan¯ly)j х 1 + y?, across the cardioid…

A:

Q: If the vector field F = (sinx + (7 + c)xy, (c + 1)x² – e') is conservative, then c=

A: Given

Q: Verify if the vector field F = (x° cos(4y), -x sin(4y)) is conservative and evaluate the line…

A:

Q: Consider the line integral cos(x+2y)dx+2cos(x+2y)dy where S is a curve starting at (0,0) and ending…

A: We have to show that F is conservative. When F is given as F=cosx+2yi+2cosx+2yj For the conservative…

Q: Suppose you need to integrate the vector field v = (3 cos z, e"+y, sin(y²)) along the curve…

A:

Q: The circuitation of the vector field F(x, y)- (3 + xy´, 4x + xy) along the boundary of the plane…

A: The solution are next step

Q: Is the vector field F(x, y) = (sin(x)ely=3 + 2r cos(r>)y°, -2e)y-3 + 6 sin(x³)»*) conservative?…

A: Consider the given vector field.

Q: 1,1,0 ex 0,0,0 Show that the vector field defined under the integrals e koct and that the scaler…

A:

Q: Find the work done by the field F(x,y, z) = (6z, 12x, y?) along the curve r(t) (cos(t), sin(t),…

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Q: Compute the Laplace transform of integrate t to 0 te ^2t sin 2t dt

A: Given  : f(t) = t e2t sin2t To Find : laplace transformation Lt e2t sin2t

Q: Is the vector field F(x, y) = (6ry cos(3x²y + e*) +e* cos(3x?y + e*), 3x² cos(3x²y + e*))…

A:

Q: What is the value of the line integral on the field 5xy? 5æ?y F(x, 3) = ()i+ ( 2 along any path from…

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Q: 2的 在年

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Q: du d'u cos(-t) du 2- + u(x) = Cos I-2 du dr? sin(a-t)dt, rp u(0) = 0, u' (0) = 0. %3D

A:

Q: Find the curl of the vector field F = (3x sin(y), 7y cos(x)).

A: The solution is:

Q: Question 3 (2y +z z2 Give line integral of vector field v(x,y,z) = along curve y: ř(t) = | -t),t E…

A:

Q: (2) Find the line integral of the vector field F(x, y) = (-1,3) along the path from (2, 3) to (2,…

A: The vector field F→=-1, 3To find line integral of vector field along the path 2, 3 to 2, 5

Q: For what values of a and d does the vector field F = ⟨ax, dy⟩ have zero flux across the unit circle…

A: A vector field, have zero flux. Across the unit-circle centered at the origin and oriented…

Q: 1.) Given the conservative vector field F(x,y,z) = ( y In z,x In z, xy find the work required to…

A: The conservative vector field Fx,y,z=y ln z, x ln z, xyz. The parametric equation of line segment…

Q: 2. Find the gradient field F = Vy for the potential function p. Sketch a few level curves of o and a…

A: Given φ(x,y)=2x2+4y2 The gradient field  F=∇·φ=∂φ∂x,∂φ∂y=4x,8y Some vectors of F are  At x=1 and y=1…

Q: e**(ysinleldx+xsinlaldy + cos l2) dz 0,0, TT Show that the vector field defined under the integral…

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Q: Express the field D = (x2 + y)-(xax + yay) in cylindrical components

A:

Q: TRUE OR FALSE? The line integral of the given vector field F along the curve that is circle C is…

A: Calculate curl of the vector function:  ∇×F=k→∂∂x2arctanyx-∂∂yy-lnx2+y2…

Q: Find the flux out of the curve bounded by the top half of = arccos(√√²+² ) and y=0 with vector field…

A: As per the question we are given a bounded curve C and a 2d vector field F And we have to find the…

Q: 6. Compute ſ, F-·dr where f(x, y) = (y² cos x, 2y sin r) and C is the straight line path starting at…

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Q: Find the directional derivative of the field f(x, y, z) = -4x³ + 3 xy² + 5 y³ at P = (-1,–3,5) in…

A: Given f(x,y,z)=-4x3+3xy2+5y3  we have to find directional derivative of f at P=-1,-3,5 in the…

Q: 5) Integrate the vector field h a,y)= y2i+ (2xy-e*)J C parumetrizal by t€ £0, 5 3. over the circular…

A:

Q: 43 Find the work done by the force field F(x, y) = (x² ln(y + 5), -) on a particle 3(y + 5) that…

A: Given force field F(x,y)=x2ln(y+5),x33(y+5) and circle x2+y2=4. The objective is to find the work…

Q: du du du + u(x) = cos r- 2- cos(-t) d'u dt-2 / sin(a-t) dt, 2 dt dr? u(0) = 0, u'(0) = 0.

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Q: Evaluate the line integral of the vector field F = xy²i+ x²yj along the curve r(t) = (t+sin,t+cos-…

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Q: 2: Compute the work done by the force field F = (y, -x) to move an object from point A = (1,0) to B…

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Q: Find the flow of the velocity field F = b. a. Na g (2,8) : 4x (0,0) X (5y² + 1)i + (10xy)j along…

A: