3. Use the Divergence Theorem to evaluate F.dS where F = -zyi+(z – 1) j +k and S is the surface of the solid bounded by y = 4z +4:2 –1 and the plane y = 7. Note that both of the surfaces of this solid included in S.

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: 1. Find fF. dr where f(x, y, z) = (3x²y, r³, 3ry) and C is the curve obtained by intersecting the…

A: The given function is  and the surface is bounded by the curves  and .Find  as follows.Put .So, the…

Q: Find an equation for the tangent plane to the surface z = 6x3y2 + 3y at the point P(1, -3). Hint:…

A:

Q: Q1// Evaluate , F ds where F = yi + xj + 4zk and S is the surface x? + y? = 9 in the first octant…

A:

Q: 2. Let S be the surface given by r(u, v) = (u, u² + v², v). Find the equation of the tangent plane…

A:

Q: Determine the point(s) on the surface z = e(3x² +9y2) at which the tangent plane is parallel to the…

A:

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: Find the equation of the tangent plane to the surface y = 2x2 – z2 at the point (0, –1, –1) y+ 4z =…

A: We have to find

Q: b) Use Gauss theorem to evaluate F.ndS, where F(r, y, 2) = (2x²y² + In z) i – xy³ j – tanh(a² + y³)…

A:

Q: (b) What is the sample median of the six values above? 051 053.5 059 058.5 055.5

A:

Q: 1 Find the inverse of the matritift eaists, If it does mot erist.wdle DO ES 'NOT EXIST dnd explain…

A: Given: Let A=-27651-2384

Q: 4. Consider the surface defined by the portion of the cone z = -Vx2 + y? that lies below the…

A:

Q: 12. Let C represent the curve of intersection between the cylinder x² + y² = 4 and the plane z = 10…

A: The plane z=10-x will cut the cylinder x2+y2=4 to give an ellipse.

Q: c) Use Stokes' theorem to evaluate where F(x, y, z) = (x²+y²z) i+(x²+xy²) j+(x²+z²) k, and C is…

A:

Q: (a) Show that the two surfaces S₁: z = xy and S₂ : z = ³x² - y² intersect perpendicularly at the…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other questions as…

Q: 2. For the surface z = In(y+ Vx² + y²). (b) Find the linear approximation at the point (3,-4).

A:

Q: p: It is snowing. q: Laura is wearing gloves. r: It is spring. For each part below, fill in the…

A: The statements given are p : It is snowing.q: Laura is wearing gloves.r: It is spring. Then the…

Q: b) Given F(x, y, z) = (x³ + cosh z) i+(2y³ – 3x²y) j – (x² + 4y²z) k. Use Gauss's theorem to…

A:

Q: Evaluate f(V x F) dS where S is the surface x² + y² +3z² = 1, z ≤0 and F = (y, -x, zx³y²). Let the…

A:

Q: 1. Let S be the portion of the surface x² + z² = 1 lying in the first octant and bounded by x = 0, y…

A: