Let C be the upper half of the circle whose equation is x2 + (y - 2)2 that is generated by revolving curve C along the x-axis. Describe S using a vector function of 2 = 1. Let S be the surface 3 3/3 variables and find an equation of the plane tangent to the surface S at the point (0, ).

Q: Find a vector tangent to the curve of intersection of the two cyclinders x2 + y2 = 50 and y? + 22 =…

A: Find a vector tangent to the curve of intersection of the two cylinderx2+y2=50 and y2+z2=50 at the…

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Q: Find a vector function that represents the curve of intersection of the paraboloid z = 7(x^2) +…

A: We have to find vector function that represents the curve of intersection of the paraboloid z =…

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A: Equation of tangent plane

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A: Given surfaces are And the given point P is

Q: Find an equation of the sphere with center (2, 1,−3) that is tangent to the plane x −3y + 2z = 4.

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Q: Find parametric equations for the tangent line at (1, 3, 3) to the curve of intersection of the…

A: First, find the function of the surface in three variables, f(x,y,z).  f(x,y,z)=x2y-z Find the…

Q: Find the vector equation of the plane tangent to the surface z = x^3 - y^3 at the point (0,1,-1)

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Q: Find the equations of the normal line and the tangent plane to the parametric surface defined by the…

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Q: Find an equation of the plane tangent to the surface

A: Given that : The equation is x2 + y 2 z 2 = 8 and the point P = ( 2, 2, 1).

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 =1 16 at the point (1,-3,2) O a. 3x-2y+z=24 O…

A: Given: x24+y29+z216=1 x,y,z=1,-3,2. Simplify the equation.…

Q: Ř(u, v) = (u², v – 2u, u + v²)

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Q: Find the equation of the tangent plane to the parametric surface x = u², y = u- v?, z = v² , at the…

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Q: If a curve has the property that the position vector r(t) is always perpendicular to the tangent…

A: given that, a curve has the property that the position vector r(t) is always perpendicular to the…

Q: Find an equation for the plane that is tangent to the surface z= Vy - I at the point (2, 3, 1).

A: We have to find partial derivatives first.

Q: Two plane curves are defined by the vector functions r1(t)=⟨t,2t−4⟩ and r2(u)=⟨2u,u2⟩. Find the…

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Q: Sketch the curve associated with the vector function r(t) = . Hint: Show it lies on the surface z?…

A: Given the vector function is r→t=tcost,tsint,t. Skecth the curve associated with the above vector…

Q: The normal vector to the tangent plane for the surface x²y³ z = 8, at the point (-1, 2, 1) is: 2 3…

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Q: Which of the following vector functions represents the curve of intersection of the cylinder x2 +y =…

A: Given Data: The equation of the curve is: x2+y2=4 ......1 The equation of the plane is: x+z=3…

Q: Let S be the surface described by the vector function Ř(u, v) = (v², u + v, e²«). Find an equation…

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Q: Find equations of the normal line and the tangent plane to the parametric surface defined by the…

A: NOTE: Refresh your page if you can't see any equations. . the given point is  compare coordinate on…

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. x = u…

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Q: Give the length of a curve given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in…

A: given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in the vector form.

Q: Find the equation of the tangent plane for the surface z = xy at the point (-1,2,-2) O z=x-2y+2…

A: The equation of tangent plane for the surface z =f(x,y ) at point (m,n,f(m,n)) is given as:

Q: Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin,…

A: Solution: Given, Circle having center at (0, 0) and radius is 5 and

Q: The two surfaces x2 + y2 + z2 = 6 and 2x² + 3y2 + z2 = 9 intersect at the point(1,1,2). Find the…

A: Given: The two surfaces  x 2 + y 2 + z 2 = 6  and  2 x 2 + 3 y 2 +  z 2 = 9. The given two surfaces…

Q: Consider the line perpendicular to the surface z=x^2+y^2 at the point where x=3 and y=2. Find a…

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Q: The two surfaces x2 + y2 + z? = 6 and 2x2 + 3y2 + z2 = 9 intersect at the point(1,1,2). Find the…

A: We have to find angle between two tangents - First we will find divergence of function f at point…

Q: Find a unit vector n that is normal to the surface 4z? – 2x* – y = 18 at P = (1,2,3) that points in…

A: Solution of question is written in below steps.

Q: Find an equation of the tangent plane to the parametric surface. x = u + v, y=6u^2, z = u − v. at…

A: Find an equation of the tangent plane to the parametric surface. x = u + v, y=6u^2, z = u − v. at…

Q: The normal vector to the tangent plane for the surface xy² z³ 2 3 = -4, at the point (1, 2, -1) is:…

A:

Q: Let C be the curve of intersection of the surfaces with equations   x2 + y  =  5   and   24x + 4y…

A: Given: Let C be the curve of intersection of the surfaces with equations x2+y=5  and   24x + 4y + z…

Q: (a) Find equation of the tangent plane and normal line to the sphere x + y +z = 25 at the point…

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: B-For the surface z² = x² + y² find the directional derivative at the point (√2, √2,-2) in the…

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Q: Find a vector equation for the curve of intersection of the surfaces x^2 + y^2 = 4 and z = xy.

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Q: Find rectifying plane of et, é, t at the curve t%3DL

A: Given curve is αt=et,e-t,2t.  To find the rectifying plane of the curve . Result: Let rt→=xt,yt,zt…

Q: Find a vector function that represents the curve of intersection of the paraboloid z = x^2 + y^2 and…

A: Intersection of paraboloid and cylinder can be obtained by representing y in the form x and z in the…

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Q: Sketch the curve of intersection of the surfaces, and find a vector equation for the curve in terms…

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Q: he normal vector to the tangent plane for the surface point (1, 2, -1) is: Select one: None of them…

A: topic:- application of derivatives

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A: Dear student. You have posted many parts, according to the policy we will answering the first part.…

Q: Find a vector function that represents the curve of intersection of the surface 4x+2y-8z^2=16 and…

A: To find a vector function that represents the curve of intersection of the surface 4x+2y-8z2=16 and…

Q: 2. Find an equation of the tangent plane to the parametric surface F(u, v) = (, 2uv, uv?) at the…

A: (2) Consider the provided question,

Q: Sketch the curve of intersection of the surfaces, and find a vector equation for the curve in terms…

A: First, we will sketch the curve of the intersection of the surface. The equation of the surfaces are…

Q: What is the perpendicular vector to the surface f(x.y.a)-ay-3r+'y-0 at (1,-1,2)? (3,3.0) (1,1.3)…

A: A vector that makes an angle of 90 degrees with the given surface is said to be perpendicular to the…