7. Find the equation of the tangent plane to each surface at the given point. (a) x? + y? + z² = 14 at (3,2, –1). (b) x² + y? = z² + 1 at (1,1,1).

Q: 32 – x² – 3y² at the 5. Find the equation of the tangent plane to the surface z = point (2, –1, 5).

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

A: Topic:- application of derivatives

Q: Find an equation of the tangent plane to the surface z = x^3- y^2 + 12x + 2y at the point (1, 2, 5).

A: Given: z = x^3- y^2 + 12x + 2y (1, 2, 5)

Q: Find the equation of the tangent plane to the surface 2= 42 + 3y+7zy at the point (0,-1,3).

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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 of the tangent plane to the given surface at the specified point. z = y cos(x - y),…

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Q: Find an equation of the tangent plane to the surface given by z² – 2x2 – 2y? = 12 at the point (1,…

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Q: 3. Find the equation of the tangent plane and normal to the surface z =x? +y? + 4 at point (1, -1,…

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Q: Find the equation of the tangent plane at the point (1, 2, 7) to the surface given by x³ sin(z) +…

A: Consider a surface F(x,y,z)=0. Then the equation of the tangent plane to the surface F at the point…

Q: 4.) Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

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Q: Find the equation of the plane tangent to the following surface at the given points. x² +…

A:

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 an equation of the tangent plane to the surface z = x2 + y2 + 2 at the given point (1, 3, 12)

A: Given surface, So

Q: Find an equation of the tangent plane to the given surface at the specified point. z = 2x2 + y2 -…

A: We know that equation of tangent plane to the surface z=f(x,y) at the point (a,b,c) is

Q: 1. Find an equation of the tangent plane to the given surface at the indicated point. 2² + y? – 3z =…

A:

Q: Find an equation of the tangent plane to the given surface at 'the specified point. Z =2x²+y&-5y and…

A: The equation of a tangent plane to the surface f(x,y,z) at the point x0 , y0 , z0 is calculated…

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

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Q: Find the equation of the tangent plane to x2 the surface z = 4 + y? at the point (2, –2, 5)

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Q: Find the equation of the tangent plane to the surface z = 4 号+ゾ + y² at the point (2, -3, 10)

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Q: Find an equation of the plane tangent to the following surface at the given point. z = 6 - 4x2 - y2;…

A: By using equation of tangent plane for surface, we calculate the required tangent plane.

Q: Find an equation of the tangent plane to the surface at the given point. x^2 + 3y^2 + 4z^2 = 20, P =…

A: The equation of the tangent plane can be calculated by using the formula…

Q: 1. Find an equation of the tangent plane to the surface of z = sin(x - 2y) at the point (7,2,0).

A:

Q: 12. Find an equation for the tangent plane to the surface given by 2xy? = 2z2 – ryz at the point (2,…

A: We know that the equation of the tangent plane is: nxx-x0+nyy-y0+nzz-z0=0 Where n→-nxi+nyj+nzk is…

Q: Find an equation of the tangent plane to the given surface at the specified point. z = 6(x − 1)2 +…

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Q: Q3/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 an equation of the tangent plane to the given surface at the specified point. z = In(x - 3y),…

A: Here, the surface is: z=ln(x-3y) To find the equation of the tangent plane at the point (7,2,0).…

Q: Find an equation of the tangent plane to the given surface at the specified point. z = 4(x - 1)² +…

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Q: Find an equation of the tangent plane to the surface at the given point. z = 5 - 2x - y, (3,-1, 1)

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Q: Find the equation for the tangent plane to the surface z=-8x2 -4y2  at the point   (2,1,-36)

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Q: Find an equation of the tangent plane to the surface at the given point in the figure below.

A: Consider the given:…

Q: Find the equation for the tangent plane to the surface z=-8x2 -4y2 at the point (2,1,-30)

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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: Find an equation of the tangent plane to the given surface at the specified point. z = 4(x - 1)2 +…

A: We have equation of the form     z= f(x, y)  And we have to find equation of tangent plane to the…

Q: Find an equation of the tangent plane to the given surface at the specified point. z3 бх2 + у2 - 7у,…

A: Solved below...

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

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Q: 4. Find an equation of the tangent plane to the surface x = u? + 1, y = v + 1, z = u + v at the…

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

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

Q: 22 2 Find the equation of the tangent plane to the level surface xy*z? (– 1, – 1, – 2) = 4 at the…

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Q: Find the equation of the tangent plane and normal line to the surface at the given point. x2 z = 9…

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Q: Find an equation of the tangent plane to the surface z = 24 3z+4y at the point (4,3, 1).

A: Use equation of tangent plane

Q: Find an equation of the tangent plane to the surface at the given point. z = x2 + y2 + 4, (1,2, 9)

A: We know that the equation of tangent plane to the curve z=f(x,y) at point (a,b,c) is

Q: Find an equation of the tangent plane to the surface at the given point. z = 8 – (3, –4, 4)

A:

Q: 7. Find an equation of the tangent plane to the given surface at the specified point. cos(x –…

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Q: 3. Find the equation of the plane tangent to xyz + x² – 2y² +z' =14 at (5,–2,3)

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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 the tangent plane to the surface z = x² +y² + 1 at the point (1,1,3). Write the…

A: use the equation of tangent  plane for the given surface.

Q: Find an equation of the tangent plane to the given surface at the specified point. z= e(x^2)-y2,…

A:

Q: Find an equation of the tangent plane to the given surface at the specified point. z = 6x² + y² -…

A: This question is based on finding equation of plane to the given surface at a point.

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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Q: Find an equation of the tangent plane to the surface at the given point. - . z = 8 —х — у, 3 (3, –4,…

A: Given plane is z=8−83x−y. We have to find the equation of tangent plane to the surface at the point…