2. Find equations of the normal plane and tangent line to the curve of intersection of the surfaces defined by S: z 2x-xy and S2: xy+yz+xz =3at the point (1, 1, 1).

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: 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 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: (4) The equation of the tangent plane to the surface In = z²(x – 2y) + 3z +3 at (4, 2, –1) is 2y

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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: 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 equation of the tangent plane to the surface z = f ( x , y ) = x 3 − 2 x y + 5 y 2 at P (…

A: Given: The equation of the surface  z=f(x, y)=x3-2xy+5y2. The point P2, 1, 9.

Q: Consider the normal line to the surface z = x2 + y² (paraboloid) at the point P(1, 1, 2). Find the…

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Q: 5. Show that the equation of the tangent plane to f(r, y, z) = c at (ro, yo, 20) is given by the…

A: Given: Surface f(x, y, z)=c and a point x0, y0, z0 To show: Equation of tangent line to f(x, y, z)=c…

Q: f(7,9) = 7. (1,1,1) zx/2+ y/2+5 -4/8-y/2

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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: Let F(x, y, z) =7x2+8y2+13z2. Find the equation to the tangent plane to the level of surface F(x,…

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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: Find the equation of the tangent plane to x² the surface z = + y? 4 - at the point (2, 3, 10) x + 6y…

A: The equation of the tangent plane to a surface f(x,y,z) is given by:

Q: Suppose that the plane tangent to the surface z = f(x, y) at (-4, 2, 5) has equation z + 5x + 4y =…

A: From the equation of tangent, we can derive: z = -(7 + 5x + 4y) Hence,

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

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Q: For the level curve f(x,y,z)=12 for f(x,y,z)= 4x2 − 2y2 + z2 at the point (2,2,2), find the…

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Q: Find the plane tangent to the given surfaces at the specific point f(x, y) = x2 ln(2x+y) in (-1, 3)

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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 all points on the surface at which the tangent plane is horizontal. (a) z = x³y² (b) z = x² −xy…

A: (a). Given the surface z=x3y2,the tangent lane at a given point is given by :…

Q: Find an equation of the tangent plane to the surface z= z + 2y² at the point P(1, 1, 3). Nind th…

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: Consider the surface x2 + y2 − 2xy − x + 3y − z = −4 and the point P(2, −3, 18). Determine the…

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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…

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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: At what point on the paraboloid  y= x^2 +z^2is the tangent plane parallel to the plane x+2y+3z=1 ?

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Q: Find the equation of the plane tangent to the grapl UI z = f(x, y) = x² + 2y³. + 1 at the points in…

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Q: Find an equation of the tangent plane to the given surface at the specified point z = √√√xy, (3, 3,…

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Q: Find an equation of the tangent plane to the given surface at the specified point. z = 4x2 - y2 +…

A: The equation of tangent plane to the surface z=f(x,y) at any point (a,b,c) is…

Q: 9. Show that the sum of the T-, y-, and z- intercepts of any tangent plane to the surface VI + Vỹ +…

A: Given, Gradient of the surface at any point (x0,y0,z0) is given by,

Q: Find an equation of the tangent plane to the given surface at the specified point. f(x,y) =…

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Q: Find an equation of the tangent plane to the given surface at the specified point. z2 = x2 + y?,…

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

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Q: Find the point on the surface  z=x2−y2  at which the tangent plane is parallel to the plane…

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Q: Find an equation of the tangent plane to the surface f(x, y, z) = x 2 + y 2 + xy − yz − xz + z 2 − 2…

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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: 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: Find the equation of the plane tangent Z= x2+ Y2 at point P (1,2,5) to the surface

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

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: 3. Find an equation of the tangent plane at P = (0, 3, –1) to the surface with equation ze" + elz+1)…

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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: 30. The equation of the tangent plane to the surface z = x? – 2y² at x = 1, y = 0 is (а) 2 — : 2т —…

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Q: Write the equations of the tangent plane and the normal line to the surface y + In(xz) Z = at the…

A: I have appended the formula used in the solution part

Q: Find an equation for the tangent plane to the surface z = 3y^2 − 2x^2 + x at P(2, −1, −3). Express…

A: Let's find equation of tangent plane.

Q: Find an equation of the plane tangent to the surface f(x, y) = xy² – 5x at the poin (1, 2, –1).

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

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 the equation of the tangent plane to the surface 4. =1 at the point 16 9. (1,-3,2) O a.…

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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: 3. Find the equation of the tangent plane to the surface in R³ defined by z = 2x² + y² at the point…

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