2. For the surface z = In(y+ Vx² + y²). (a) Find an equation of the tangent plane at the point (3, -4).

Q: ind the equation for the tangent plane to the surface z = In(6x2 +9y2 + 1) at the point (0,0, 0).…

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Q: The horizontal tangent plane of the surface z = 2x² – xy – y² + 6x – 6y – 2 is given by the equation…

A: Consider the given equation. z=2x2-xy-y2+6x-6y-2 Find the derivative with respect to x and y.…

Q: 3. Find the equation of the tangent plane to the given surface at the point (0,-1,-2). y = 2x? - ? O…

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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 the point(s) on the surface z = 3 − x2 − y2 + 6y, at which the tangent plane is horizontal.

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Q: Find the equation of the plane tangent to the surface G(x,y, z) = 2x² - y² – 3z2 = -4 at P = (-2,…

A: Given surface is                                                G(x, y, z): 2x2-y2-3z2=-4 we have to…

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

A: The given function is It can be written as as the given function has both variables x and y.

Q: Find the slope of the tangent line to the curve that is the intersection of the surface z = x2 - y2…

A: Calculate point of intersection and differentiate it to get the answer

Q: find an equation for the plane that is tangent tothe given surface at the given point. z = √(y - x),…

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Q: Find the equation for the tangent plane to the surface Z =-8x² - 3y2 at the point (2 1, -35). O 2x +…

A: We can find the answer as below

Q: z = In (x² + y²) at point Po(1,0, 0).

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Q: The horizontal tangent plane of the surface z = 4x – xy – 2y – 2x – 8y – 3 is given by the equation…

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Q: Consider the surface z = 2 – xy in R³. Use the second derivative test to find the points on this…

A: Given curve z = 2-xy To find :- Use the second derivative test to find the points on this surface…

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: Picture attached. Thanks in advance!

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Q: Q4) given the surface: cos nx – x²y + exz + 2yz = 2 Find the equation of the tangent plane and…

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Q: Find the points at which the following surface has horizontal tangent planes: x² + 2y² + z2 – 2x –…

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Q: 9) Find a point on the surface z = 8- 3x2 - 2y2 at which the tangent plane is perpendicular to the…

A: In this question we have to find a point on the surface at which the tangent is perpendicular to the…

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: Find the points on the surface ry + yz + zx – x - 22 = 0 where the tangent plane is parallel to…

A: Given surface is  Fx, y, z=xy+yz+zx-x-z2 and we have to find the points on this surface where the…

Q: 4. Find both points on the surface xz – x2 – y? = 8 where the tangent plane is horizontal.

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Q: Find equation of the tangent plane to the given surface at the specified point. 5x^2+3y^2+8z^2,…

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Q: Find the equation of the tangent plane to the surface determined by z'y' + z – 25 = 0 at z = 4, y =…

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Q: Find the equation for the tangent plane to the surface -3x+ 9y -7z = -26 at the point (1,-1, Lütfen…

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Q: Find equations for the a) tangent line and b) normal plane to the curve made by the intersection of…

A: Given The given surfaces are 3x2y+y2z=-2 and 2xz-x2y=3.  The given point is 1,-1,1.

Q: Find the equation of the surface of revolution of x = z2 about the x-axis.

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Q: Find an equation of the tangent plane to the surface zx + 2xy + 3yz3 = 6 at a point in the…

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

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Q: Sketch the section of the surface at y=0. z = /2+x² + y?

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Q: Find the equation of the tangent plane to the surface z = In (2x + y) at the point (-1, 3, 0) . O x…

A: The equation of the tangent plane to the surface Z=fx,y atthe point a,b,fa,b is given by…

Q: Find a point on the surface z = 3x^2 − y^2 at which the tangent plane to this surface is parallel to…

A: We need to find the Point on the surface of  z=3x2−y2 given tangent plane to this surface is…

Q: The equation of the tangent plane to the surface defined by z y exp(-x) at the point (0, 1, 1) is =…

A: equation of the tangent plane

Q: Find the equation of the tangent plane to the sphere x² + y2 + z² = 1 at the point (1/ V3, 1/V3, 1/…

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Q: Find the point(s) on the surface z = 3x2 + 2y2 − 3x + 4y − 5, at which the tangent plane is…

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Q: 4. Determine all points on the surface x² + 2y² + 3z² + 2xy + 2yz = 1 in which the tangent plane of…

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Q: Find an equation of the tangent plane to the surface given implicitly by z= sin(zy) at the point (,…

A: A tangent plane to a surface is a plane that just touches the surface at a single point. The…

Q: Find the equation of tangent plane to the surface x² + 2y? + 3z2 = 21 which is parallel to the plane…

A: Topic- equation of tangent to surface

Q: 9) Find a point on the surface z = 8 – 3x2 – 2y² at which the tangent plane is perpendicular to the…

A: Given, Surface, z=8-3x2-2y2 at which the tangent plane is perpendicular to the line…

Q: 3/Find the equation for the tangent plane and normal line to the surface Z=9-x² + y² at the point…

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Q: Find the equation of the tangent plane to the surface 3D1 16 at the point (1,-3,2) O a. 2x+4y-3z=12…

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Q: Find the equation for the tangent plane to the surface z=In(9x2 + 5y2+1 O x+y = 0 z = 0 O x-y = 0 O…

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Q: Find the equation of the tangent plane to the surface 2x^2 -xz + y^2 -zy = -5 at the point (1, 3, 4)

A: First we find out partial derivative at given point and then find the equation of the tangent plane…

Q: (b) Find the point that makes the tangent plane to the surface z = x- xy +y-2x + 4y horizontal.

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Q: Find the equation of the tangent plane to the given surface at the point (0,-1,-2). y = L - O + 2z =…

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Q: Find the equation of tangent plane to the surface x? + 2y? + 3z2 = 21 which is parallel to the plane…

A: equation of the tangent surface of  F= x2+ 2y2+ 3z2= 21   which is also parallel to the plane…

Q: Find an equation of the tangent plane to the surface z = xy at (1,2,2).

A: The given surface can be written as F(x, y, z)=0, where F(x, y, z)=xy-z

Q: Find the angle of inclination of the tangent plane to the surface 3x2 + 2y2 − z = 15, at the given…

A: We have given surface 3x2+2y2-z=15 at point (2, 2, 5)   We have to find the angle of inclination…

Q: Find the equation of the tangent plane to the surface xy + 2yz + 3zx = 11 %3D at the point P (1, 1,…

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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: 14. Find a point on the surface z = 3x- y at which the tangent plane is parallel to the plane 6x +…

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