Let f(x,y,z)=-x^2+sin(y)-2z^2=0 define a surface in 3 dimensions. Find the equation of the normal line to the surface in 3 dimensions.  Find a point which is at a distance of 4 from the tangent plane at the point (2pi, 0, 3/2)

Q: Find the points on the surface xy + yz + zx - x - z2 = 0 where the tangent plane is parallel to the…

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Q: Find the area of the surface x2 + y2 - z = 0 that is cut from above by the plane z = 4

A: Surface is given by x2+y2=z Area=∫∫R2x2+2y2+1dA       =∫∫R4x2+4y2+1dA Let x=rcosθ and y=rsinθ…

Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface.3.…

A: To find equations for the(a) tangent plane and(b) normal line at the point P on the given surface.…

Q: Find a point on the surface x+4y--z² =1 where the tangent plane is parallel to the plane x+4y- z =…

A: we need to find gradient of given surface to know about direction of normal vector to tangent plane

Q: * = Vy +5,

A: We have to evaluate the area of the surface generated by revolving the curve  x=y+5 between the…

Q: Find the tangent plane and normal line to the surface f (r, y) = In (2r + y) at the point (-1,3,0).…

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

Q: Find the area of the portion of the cylindrical surface y = 4 – x² in the first octant that is…

A: Find your answer below below

Q: Find the points on the surface ( y + z)^2 + (z - x)^2 = 16 where the normal line is parallel to the…

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Q: Find the area of the surface obtained by rotating the curve }=2,3 from z = 0 to z = 1 about the…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. X = 2 + 3y2, 1 <…

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Q: Determine if the surface x^2 + y^2 +z^2 = 1 is tangent to the surface x^2 + y^2 + z^4 = 1 at…

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Q: Find a unit normal to the surface x'y + 2xz = 4 at the point (2,-2,3).

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Q: 2. The surface area of the surface generated by revolving the curve y = x, -1 < x<1, about the…

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Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: We need to find points of intersection.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.  x=1+5y2,…

A: Recall: Area of the surface rotating about the x-axis: If the curve x=g(y) is given , c≤y≤d , and…

Q: Show that the line normal to the surface xy + z = 2 at the point (1, 1, 1) passes through the…

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Q: Let h(x, y) = xye-(x²+y²). Classify all local extrema of the surface using the second derivative…

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Q: An equation of the tangent plane to the surface z = In(x - 2y) at (3, 1,0) is given by z = x + 2y- 1…

A: This question is related to three dimensions geometry.

Q: Find the exact area of the surface obtained by rotating the curve x = (1/3)y^3, 0 &lt;= y &lt;= 1,…

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Q: Consider the surface x^4+ 3xz + z^2+ cos( πxy ) = -2 and the point P0 ( -1, 1, 2) on that surface.…

A: Given the equation of surface x4+3xz+z2+cosπxy=-2 at point P0-1, 1, 2. The equation of tangent plane…

Q: Find the area of surface x2 – 2y – 2z = 0 that  lies above the triangle bounded by the lines x = 2,…

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Q: Determine the equation of the normal line to the surface z2 cos(x + 2y) at the point (2, –1, 0).

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Q: #3) Find equations of the tangent plane to the given Surface at the specified Põint. X + y +Z=42VZ…

A: Find the equation of the tangent plane.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x, 0s x< 3

A: The objective is to find the surface area.

Q: 4. Consider the surface given by z = x x²esin y. (a) Find the equation of the tangent plane to z =…

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Q: 4. Find the area of the surface obtained by rotating the curve x²/3 + y>/3 = 1, 0 <y<1 about y-axis.

A: If the curve defined by the parametric equations x=x(t), y=y(t)  with a≤t≤b , is rotated about the…

Q: Find the equation of tangent plane and normal lines of the surface: ( x, y, z) = 5x^2 +  4y^2 + z^3…

A: We have to find the equation of tangent plane and normal lines of the surface: f(x,y,z)=5x2+…

Q: The area of the surface obtained by rotating the curve y = V16 – x² -1 <x< 1, about the x- axis is

A: The given function is y=16-x2 , -1≤x≤1 rotating the curve about x-axis.

Q: Find an equation of the tangent plane and a parametric description of the normal line to the surface…

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Q: Find equations of the normal plane and tangent line to the curve of intersection of the surfaces…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 1 + 2x 1 < x< 1…

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Q: Find the area of the surface that is generated by revolving the portion of the curve y = x2 between…

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Q: Find the equation of the tangent plane at the point x = xo = 4, y = yo = 1 of the surface %3D z =…

A: Option C is true

Q: Find the parametric equations of normal line to the surface given by f(x, y) = tan v x2 +y2 at the…

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Q: The area of the surface obtained by rotating the curve y = √√x + 1, for 0 ≤ x ≤ 2, about the x-axis,…

A: Given :

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 5 + 4y2,…

A: We use the formula S=2π integration of y √(1+x'2)dy from 1 to 2

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 1 + 2x < x < 1 y…

A: Surface area of curve by using integration

Q: Find the area of the surface that is generated by revolving the portion of the curve y = x2 between…

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Q: 1) Let h(x, y) = x* – 4xy² – 2x² + 8y². Find and classify all local extrema of the surface using the…

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Q: 3. Consider the surface sin (xy)+ cos (xz)+sin ( yz) =1. Find an equation for the tangent plane to…

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Q: x = 1+ 2y2, 1< x < 2 about the x-axis.

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Q: Sketch the section of the surface at z = 0 on y = sinx in xy-plane on [0,2x]. y = sinx 1 3 4 5 1 1 2…

A: Let's find.

Q: b) Find the equations of Tangent plane and Normal line of the surface: z3 + xyz – 2=0 at Po(1,1,1)

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Q: ii) Find the exact area of the surface obtained by rotating the curve 1 12x 3 y = x³ + 9 1 ≤ x ≤ 2,

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Q: Suppose that f(1, 0, − 1) = 2, and f(x, y, z) is differen- tiable at (1, 0, -1) with Vf (1, 0, -1) =…

A: We have to find out equation of tangent plane and parametric equations of normal at point (1,0,-1)…

Q: Determine the equation of the normal line to the surface z2 = cos(x + 2y) at the point (2, –1,0).

A: We have  z2 = cos(x+2y) ⇒cos(x+2y) - z2 = 0  So, F(x,y,z) = cos(x+2y) - z2  Thus,  ∇F(x,y,z) =…

Q: 13. Find all points on the surface at which the tangent plane is horizontal. 3,,2 (a) z = x°y ² (b)…

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Q: 2. Find the area of the surface obtained by rotating the curve: y = Vx +1,1<x<5 about the Х-ахis

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Q: Find the tangent plane and normal line of the surface x+y+z=1 at the point p(0,1,0).

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