b) Given F(x, Y, z) = (x³ + cosh z) i+ (2y³ – 3x²y)j – (x² + 4y²z) k. Use Gauss's theorem to calculate F.n dS where n is the outward unit normal of o, the surface bounded by the planes, x = 0, z = 0 and TM x+ z = 6, and the parabolic cylinder x = 4 – y².

Q: Find the equation of the tangent plane (in the form z = ax + by +c where a, b, c are constants) to…

A: Here we use the formula of  ∂f∂x(a,b)(x-a)+∂f∂y(a,b)(y-b)=0 tangent plane to the surface at a point…

Q: Find the equation of the tangent plane Pr to the surface S: x2 + y? +z² = 9 at (2, –1, 2)

A: The equation of the tangent plane to the surface f(x, y, z)=0 at a, b, c is defined as: fxa, b,…

Q: Let F= (0,0, z) and S be the part of the paraboloid z = x² + y² between the plan z = 1 and 2 = 4,…

A:

Q: 7. What is the value of (X-2)2 for the scores 2,3,5?

A: To find : ∑X-22 for the scores 2, 3, 5

Q: A surface z = f(x, y) is defined implicitly by the equation x +y+ z – e² = 3 – e. - Determine the…

A:

Q: An equation of the tangent plane to the surface z = 4xy² + 3x²y² at the point (1, 1, 7) is: Select…

A: z= 4xy2+3x2y2F(x,y,z) =…

Q: The equation of the tangent plane to the surface 32 = x² + y² +1 at (-1,1,2) is O A.-2x-2y+3z = 2 O…

A:

Q: Let S be the portion of the plane 2x + 3y + z = 2 lying between the points (-1, 1, 1), (2, 1, −5),…

A: S is the portion of the plane 2x+3y+z=2 lying between the points (-1, 1, 1), (2, 1,-5), (2, 3,-11)…

Q: 3) Evaluate, to the nearest hundredth, 11. (V x F) dS where F = and S = {(x, y, z)| 2² − 1 = 3x² +…

A: Here we will use Stokes theorem  According to stokes theorem  ∫∫S∇×F.dS=∫CF.dr C is the  boundary…

Q: The surface S is defined by x + y² + z³ = 3. Find a vector normal to S at the point A with position…

A: Given a surface S the normal vector to the surface at the point A is given by

Q: The curve y = sin(πz), with 0 ≤ z ≤ 2, on the yz-plane is revolved once about the z-axis. Find a…

A: Given that y=sin πz and 0≤z≤2 The objective is to find the vector equation. The image formed is like…

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: If f(x)=14-x^(2) and g(x)=\sqrt(x+31), compute g(f(3)). Simplify your answer as much as possible.

A:

Q: Tell whether each of the following questions is biased or fair. Why? a. What type of music do you…

A: Part(a) The correct option is option A. Because in option A has the  question does not make an…

Q: 03. a. If F = (y² + z² − x²)i + (z² + x² − y²)j + (x² + y² − z²)k, then evaluate, SSV × F·n dA…

A:

Q: Consider the surface S parametrized by Þ(u, v) = (u², v², √√2uv) where 0 ≤ u ≤ 2 and 0 ≤ v ≤ 2.…

A:

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

A:

Q: x² - y²-2²-4x - 2z+3=0

A: The given surface is x2-y2-z2-4x-2z+3=0T is the trace of S using x=2.To find the two cordinate when…

Q: Find the equation of the tangent plane at the point - 2 of the surface * = 0 3, y = yo z = f(x, y) =…

A:

Q: 7. Let F(x, y,z)=-2yi +2xj. Use Stokes’ Theorem to find F dr where C is a circle (a) Parallel to the…

A: By stoke's theorem

Q: The tangent plane and the normal line of the surface x = y? + z2 + l at (3, 1, -1) have the…

A: Solve the following