2 ecos cos(send) 0 5-4 cos(6) Jo -do = 2π € 500 cos cos(sen)

Q: Consider the following statements about the surface of the equation z = 2x / (ln (y) +1) - (y + 1) /…

A: The given function is z=2xlny+1-y+1x and the given point is P-2,1. The directional derivative of a…

Q: Section 17.7) Verify Stokes' Theorem for F(x, y, z) = if C is the intersection of z = 4 + y and x² +…

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Q: Find the points on the sphere with center at the origin of radius 3 where the function f(x, y, z) =…

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Q: Suppose we have part of a hyperboloid of two sheets -4x? -4y? + z? = 9 where z 20 (so the upper…

A: Equation of hyperboloid of two sheets is: −4x2−4y2+z2=9 Where z≥0 and z≤15

Q: Evaluate ſç(2x + z², − 3y + x, 6z − 4y) · ds where S is a sphere of radius R=3 and center the axes…

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Q: Suppose z is given implicitly by the equation ln (yz2) + x3z = 1 in a neighborhood of the point P…

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Q: Starting from the point (1, −7, 0), the re-parametrization of the the curve r(t) = (1 + 3t)i + (−7 +…

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Q: 1 Evaluate f - dz over the unit circle in counter-clockwise direction using the parametriza- tions

A: To evaluate, ∮1zdz over the unit circle counter-clockwise

Q: At what point on the paraboloid y = x² + z² is the tangent plane parallel to the plane 3x + 2y + 3z…

A: Introduction: Let z=f(x, y) be the equation of a surface S in R3, and let P=(a, b, c) be a point on…

Q: The set: V = {Ae² sin (3x) + Be2 cos (3x): A, B = R} consists of all the solutions of the…

A: Given V={Ae2xsin(3x)+Be2xcos(3x): A, B∈ℝ} consist of all the solutions of the differential equation…

Q: (a) Compute directly I = S Ss F-dS, where S is the surface of the sphere x? +y? +z? = 4 and F =…

A: X²+y²+z²=4=2² Therefore radius of sphere is 2.

Q: f(x, y) = x - y“; R is the disk x +y < 1.

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Q: at P is contained within the tangent plane TpS to S at P. Find the (only) point of intersection P…

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Q: 1) Find the outward flux of F across the region D where F= (6x² + 2xy, 2y + x²z, 4x² y³ ) and the…

A: The vector field is,F¯=6x2+2xy, 2y+x2z, 4x2y3The region D is cut from the first octant by the…

Q: Figure Q4(a) shows flux for the function F = xi + yj + zk over a sphere, x? + y? + z? = 9. Determine…

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Q: Verify that the function u = is a solution of the three-dimensional Laplace equation u xx + uyy +…

A: We have been given that u=1x2+y2+z2Take partial differentiation with respect to x, we getux =…

Q: 8. Show that r(t) = a cost+bsint is an ellipse even if a and b are not orthogonal. How do you find…

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Q: Suppose that U is a solution to the Laplace equation in the disk Ω = {r ≤ 1} andthat U(1, θ) = 5 −…

A: The objective of this question is to find the value of U at the origin and the location of the…

Q: Show that the general solution to the two-dimensional Laplace's Equation. et = 0 is (Acosh(tx)…

A: We have to show that the general solution to the two-dimensional Laplace's Equation…

Q: 3) Find the curl of the vector field F(r, y, z) = (ry") i + (ya)j+ (8ry) k %3D

A: We know,If, F(x,y,z)=Fx i +Fy j+Fz kCurl of  F(x,y,z)=∇× F(x,y,z)=ijk∂∂x∂∂y∂∂zFxFyFz

Q: Find the flux of F = 3zi + 5y? i+ 3x k out of the closed cone y = Væ2 + z2, with 0 < y < 1. flux =

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Q: 3. Let F = (422, 5x, 3y). (A) Compute curl(F). (B) Parameterize each rectangular region and compute…

A: We will find curl using determinant . Then use projection on co ordinate plane to get range of…

Q: 1. Find a potential function for the vector fields a) b)

A: As per the company's guidelines, we are supposed to solve the first question for you, kindly repost…

Q: Find the flux of the vector field F = out of the closed surface S bounded by z = 5-√√x² + y² and z =…

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Q: (Section 17.6, 17.8) Consider F = xî – 2yĵ + ½ 2²k. Let S be the surface of the solid bounded by S₁:…

A: Consider the function .Let  be the surface of the solid bounded by .(a)We need to use divergence…

Q: Let W be the work (against the Sun’s gravitational force) required to transport an 80-kg person from…

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Q: (c) Part of the parabola y = 2(x + 1)² from the point (0, 2) to the point (-1,0). (d)…

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Q: The set: V = {Ae²* sin(3x) + Be² cos (3x): A, B ≤ R} consists of all the solutions of the…

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Q: Suppose that the polar coordinates of a moving particle at time t are (r(t), 0(t)). Prove that the…

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Q: 22 Find the Directional Derivabive of Pary,z)= xg-y2'+Z at the point CI, -2, 0) in the direcbion of…

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Q: 5. Evaluate the integral G. dR where G = ye*vi + (xe"y + zev² – 32) j + (yez – y+ z) k and the curve…

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Q: 4. Let Bitl be obtained from Br using the update formula (Yk – BuSk)v" Bk+1 = Br + where v is a…

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Q: 6. Let S denote the disc of radius 2 that is centered at the point (0, 0,3) and parallel to the X-Y…

A: Given that S denote the disc of radius 2 that is centered at the point  and parallelto the XY-plane,…

Q: 24. Find a parametrization of the lemniscate (x2 + y²)² = xy (see Figure 23) by using t = y/x as a…

A: Given that,  x2+y22=xy      ...(1) And t=yx⇒y=xt

Q: At what point on the paraboloid y = x + (x, y, z)=( is the tangent plane parallel to the plane 3x +…

A: The given parabola is y=x2+z2 .Let f(x,y,z)=x2+z2-y. Also the given plane  is 3x+4y+3z=2.

Q: Suppose that U is a solution to the Laplace equation in the disk Ω = {r ≤ 1} and that U(1, θ) = 5 −…

A: is the solution of the Laplace equation in the disk