Find an equation for the plane that is tangent to the surface z = In (x² + y) at the point P(0,1,0). Using a coefficient of 1 for z, the equation of the plane is = 0.

Q: Find an equation for the plane tangent to the given surface at the specified point. z = v², y = u? +…

A: Given that

Q: 3. cos Tx – x*y + e*z + yz = 4 at point Po(0, 1, 2). -

A: The given surface at the point P0 is    Cos(pix) - x2y +exz + yz = 4

Q: What is the equation of the plane to the surface z = e3y sin(3x) +2 at the point P ,0, 3 %3D O x- y…

A: The solution is given in the next step.

Q: Find an equation of the plane tangent to the following surface at the given points. zexy; (1,0,1)…

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Q: find an equation for the plane that is tangent tothe given surface at the given point.11. z = ln (x2…

A: To find an equation for the plane that is tangent to the given surface at the given point. Given…

Q: find an equation for the plane that is tangent to the given surface z = ln (x + y2),  at the given…

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Q: An equation for the tangent plane to the surface : = (xty at the point P(1, 1, 4) is a) 8x + 8y -: =…

A: Equation of a tangent to the surface z=f(x,y) at point (a,b,f(a,b)) is given by…

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Q: Let f(x, y, z) = x² + 2y? + 4z2. Find the point on the plane x + y + z = 14 at which f has its…

A: Given: fx,y,z=x2+2y2+4z2and the plane equation x+y+z=14 To find the point x,y,z The Lagrange's…

Q: Find an equation for the plane that is tangent to the surface z = In (x³ + y²) at the point…

A: Given:   A surface   z = ln x3 + y2   To Find :  An equation  for the plane that is tangent to the…

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: a) Evaluate x²y? ds, where the curve C is the intersection between the surface z = := V1– y? and the…

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Q: Find the equation of the tangent plane to the surface z = at the point (2,-3, 10) O r- 6y – z = 10…

A: We have to find the equation of tangent plane.

Q: Find an equation for the plane that is tangent to the surface z = In (x´ +y) at the point P(1,0,0).…

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Q: Find an equation for the plane that is tangent to the surface z = In (x + y²) at the point P(0,1,0).…

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Q: If (a,B.y) is a point at which the surface x2+y2-z²-2x+12=0 has a horizontal tangent plane, then y|…

A: As per guidelines, we will solve first question only. Let α,β,γ be the point on the surface…

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: Find an equation of the tangent plane to the surface z = 2a2 + 1y – la – 3y – 1 at the point (5, 3,…

A: Equation of Tangent Plane to the surface F(x, y, z) = 0 at point (x0, y0, z0) is given by ∇F(x0, y0,…

Q: What is the equation of the plane to the surface z = e3y sin(3x) +2 at the point P ,0, 3 O x - y -…

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Q: Find the point closest to the origin on the curve of intersection of the plane x + y + z = 1 and the…

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Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y2 + z?…

A: Given: Surface of revolution with the equation x2+y2+z2=e2x To find: Identify a generating curve on…

Q: An equation for the tangent plane to the surface (xty at the point P(1, 1, 4) is a) 8r + 8y-:= 0 b)…

A: The given surface is  f(x,y)=z=(x2+y2)2  ...........(1); we have to find the tangent plane at point…

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: Find an equation for the plane that is tangent to the surface z= In (x²+y^) at the point P(0,1,0).…

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Q: Find an equation for the plane that is tangent to the surface z In (x +y) at the point P(0,1,0).…

A: By using partial derivatives and tangent equation to surface

Q: Find an equation for the plane that is tangent to the surface z= In (x* +y) at the point P(1,0,0).…

A: The solution for the above question is as shown below.

Q: Find the unit normal to the surface z=2+2z^2-3y^3 at the point (1,-1,7), pointing down with respect…

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Q: Find an equation of the plane tangent to the following surface at the given points. z= eW; (4,0,1)…

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Q: Find an equation of the plane tangent to the surface z = x2 - y at the point (2, 1, 3). O A. 4x - 2y…

A: Find an equation of the plane tangent to the surface z= x2 - y2 at the point (2,1,3). Here i…

Q: Find the distance from a point P(x1, y1, Z1) to the plane Ax + By + Cz = D.

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Q: Find for the point P(x,y,z) on the plane 3x + y – z – 15 = 0 that is closest to the origin.

A: The distance of the point P(x,y,z) from the origin is: d2=x2+y2+z2 Now we have to minimize d if the…

Q: a) Evaluate y° ds, where the curve C is the intersection between the surface z and the plane x = 3…

A: Integration problem...

Q: What is the equation of the plane to the surface z = e3Y sin(3x) +2 at the point P,0, 3) O x- y + ez…

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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: Find the equation of the tangent plane to the surface z = 6x4 + 5y + 3xy at the point (-3,0, 486). z…

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Q: Find an equation for the plane that is tangent to the surface z = In (x+y) at the point P(0,1,0).…

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Q: a) Evaluate Fự ds, where the curve C is the intersection between the surface z = V1- y? and the…

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Q: Find an equation of the tangent plane (in the variables x, y and z) to the parametric surface…

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Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y2 + Z?…

A: Solution-

Q: find an equation for the plane tangent to thesurface z = ƒ(x, y) at the given point. z = 1/ (x2 +…

A: Concept - Equation of plane is given by - Ax-x0+By-y0+Cz-z0 = 0         ...............(1)where,x0,…

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

A: To find an equation for the plane that is tangent to the surface at the given point (1,2 1).

Q: Find a generating curve on the xz-plane for the surface of revolution with equation x2+ y²+ z²= e2x…

A: The solution is given below

Q: Find the distance between two planes a and a1 that are tangent to the ellipsoid 2 +2y? + z² = 5/8…

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Q: Find an equation of the surface of revolution by revolving the plane curve 3y = v(9- [(x-1)] ^2)…

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Q: The equation of the tangent plane to the surface a2- 3y2 – 22 +3 = 0 at the point (2, -1, -2) is…

A: We will find the equation of tangent plane m

Q: Find the plane tangent to the surface z=x+ y at the point (3,4,25). a. 6x+8y-z=25 b. 6x-8y-z=25 c.…

A: We have to find the plane tangent for the given surface

Q: Find any points on the hyperboloid  x2 − y2 − z2 = 6  where the tangent plane is parallel to the…

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