Consider the surface defined by the following function: x? + y? 2 = Find the points on the given surface at which the gradient vector is parallel to the vec- tor 4i +j+ k.

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. r(u,v)…

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Q: Let F(x, y) = 3 i + j + 2k, and let S be a square whose side lengths are 3, parallel to the…

A: Flux is F.dA Where F is the Field and A is the area

Q: r(u, v)=(w+v)i(u-v)j+v²k at the point P(2, 0, 1)

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: Given:

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

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Q: Let F(x, y, z) = xye" – 2° Ja and P(1,0, –1). Let S be the surface defined by the equation xye" –…

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Q: (d) Find a vector function that represents the curve of intersection of the two surfaces: the xy…

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Q: Consider x=h(y,z) as a parametrized surface in the natural way. Write the equation of the tangent…

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Q: Evaluate yds where S is the surface = x + 2y?, 0 <a < 1, 0<y S 2

A: Consider the surface, z = x + 2y²

Q: Find the equation of the tangent plane to *+ y? at the point (2, –3, 10) the surface z = 4 O x + 4y…

A: We have to find

Q: Let (S) be the surface given by the following equation. x²+y² = 1+ z?. An equation of the tangent…

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Q: 4) Find the equation of the tangent plane to the surface r(u, v) = (u²-v²)i − (3uv)j + (4√u+v)k when…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: Let (S) be the surface given by the following equation. x²+y? = 1+ z?. An equation of the tangent…

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Q: For the surface f(x,y, z) 2*y, find: The gradient of the surface at the point (1,2,1);

A: Gradient of a function

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. r(u,v)…

A: Please see the explanation below

Q: Let g(x,y,z)=5xe^y+yz^2. Use the gradient vector to find the equation of the tangent plane to the…

A: Solve the following

Q: Let f(x, y) = x² – y?. Find (b) The tangent plane to the surface given by f at the point (0, – 1).

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Q: Let F(x, y, z) = 15x? + 12y2 + 10z?. Find the equation to the tangent plane to the level of surface…

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

Q: Find an equation of the tangent plane to the surface represented by the vector-valued function at…

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Q: At which of the points below is the tangent plane to the surface z - 2y + z?+ yz = 2 vertical?…

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Q: Find a vector function that represents the curve of intersection of the two surfaces. The paraboloid…

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Q: Find the point on the surface f(x,y)=x2+y²+xy+21x+7y at which the tangent plane is horizontal.

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Q: Find an equation of the tangent plane to the surface x2 + 2y? + 3z2 = 6 at the point (1, 1, 1). O A.…

A: As we know that the equation of the tangent plane: nxx-x0+nyy-y0+nzz-z0=0 Given:…

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: The intersecting curve of two surfaces is given as follows:

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. r(u,…

A: Given, the parametric equation of surface  To find the equation of tangent plan at u=1, v=0, Now,…

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. r(u,…

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Q: Which type of surface does the curve x=t2, y = tsin(t), z=tcos(t) lie on?

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Q: Compute the flux of F= xi+yj+ z*k across the cone z =Vx2 + y? , 0szs1, in the downward direction.…

A: We have to find the flux in the downward direction.   Let us assume that x=rcosθ, y=rsinθ, z=r Then…

Q: Let f(r.y) = r'y- Find a unit vector tangent to the level curve f(r, y) = 3 at its point (1,2).

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Q: Find the outward flux across the domain D xi + yj + zk x2 +y? + z? F(x,v,z) = across the sphere x2…

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Q: Find an equation of the plane tangent to the surface xy z2 = 2 at the point (2, 1, -1). О А.х+ бу +…

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Q: Q3/ Sketch the surface z 3x2 + y? +1 and find its linear approximation at P.(0,-1).

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Q: Find a vector function, r(t), that represents the curve of intersection of the The cylinder x² + y2…

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Q: Find the equation of the tangent plane Pr to the surface S:r + y? + z? = 9 at (2, 1, –2) O Pr: 4x –…

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Q: At which of the points below is the tangent plane to the surface r2 – 2y? + z2 + yz = 2 vertical?…

A: From the tangent plane to a surface

Q: If the gradient of f is Vf = x? j – z i+ 3yx k and the point P = (-4, 3, 1) lies on the level…

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Q: Find an equation of the tangent plane to the given surface at specified poir a) z = e*y + yx²e!¬y);…

A: The formula for the tangent plane at the given point x0,y0,z0 is:…

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: First solve the given equations for finding the values in terms of x

Q: Let g(x,y,z)=2xe^y+yz^2. Use the gradient vector to find the equation of the tangent plane to the…

A: We will use definition

Q: Which of the following is a defining equation for the tangential plane to the surface defined by…

A: To find  An equation for the tangential plane to the surface defined at the point (1, 1,1)

Q: Show that the tangent plane to the surface x 2 a 2 + y 2 b 2 = cz at the point P(x0, y0, z0) is…

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Q: Evaluate || (x + y + z)dS, where S is the surface defined parametrically by S ", v) (2u + v)i+ (u –…

A: According to the given information, it is required to find the value of the integral.

Q: Find the equation of the plane tangent to the surface f(x, y) = x In(x y) at the point (1, e).

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

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Q: Let (S) be the surface given by the following equation. x²+y? = 1+z². %3D An equation of the tangent…

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Q: Find the equation of the tangent plane Pr to the surface S:r +y +z2 = 9 at (2,-1, 2) | O PT:4x + 2y…

A: The equation of the tangent plane to the surface f(x, y, z)=0 at x0, y0, z0 is defined as: fxx0, y0,…

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. r(u,…

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Q: (b) Use the corresponding formula to evaluate the line integral F. ds where F(x, y, z) = (xz, -yz,…

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