Find the slope of the surface z = f (x, y) in the y-direction at the point (64, 8).

Q: Sketch the section of the surface at y = 0. 2x + z = 3 4 -8 -6 -4 2/4 -2 6 8 -6 -8- 6. AM -8 -6 -4-…

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Q: The slope of the surface z = xy² in the x-direction at the point (2, 3) is _____, and the slope of…

A: Given:z=xy2   x-directionat the point 2, 3 y-directionat the point 2,3

Q: Find the equation of the tangent plane to the surface determined by x^3y^2+z−35=0 where x=3 and y=5.

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Q: (b) Compute the slope of the line that is parallel to the xz-plane and tangent to the surface z = x…

A: Given: Let's calculate the slope of the line tangent to the surface z=x(x+y) at the point that is…

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: The area of the surface obtained by rotating the curve y = 1sxse about the line x = 42 is

A: Given that y= 1/x  + x3 /12 and find the surface area. Here i attached solution of this question.

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: Find an equation of the tangent plane to the surface defined by the equation zf(x, y) + 2³ = 3 at…

A: The given surface is:zf(x, y)+z3=3The point is (-1, 2, 3)

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

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Q: Find the points on the surface x² −yz = 5 that are closest to the origin.

A: Let the point P be (x,y,z). The distance between the point P and origin is given by the formula…

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

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Q: Sketch the section of the surface at y = 0. 9x^2+4z^2=36

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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: Sketch the section of the surface at y= 0. z = V4 +x + y² 41 -8 -6 -4 -2 -4 6.

A: Let's find.

Q: Find the slopes of the surface in the x- and y-directions at the given point. h(x, y) = x2 − y2 (-2,…

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Q: Find the area of one side of the “wall” standing orthogonally on the curve 2x + 3y = 6, 0<=x<=…

A: To Determine: Find the area of one side of the “wall” standing orthogonally on the curve…

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 an equation of the tangent plane to the surface z = -! -3x? + 3y – 2x + 2y + 2 at the point (2,…

A: We have to find tangent plane

Q: Find the sum of the x-intercept, y-intercept, and z-intercept of any tangent plane to the surface…

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Q: Find the point on the surface f(x,y)=x2+y2+xy-16x-27y at which the tangent plane is horizontal.

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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: /Sketch the Surface Z=V9-X+y- and verify that fxg = Exx %31

A: Second order Partial Differentiation

Q: Sketch the surface given by the function. z = 9-x?-y?

A: Given, z=9-x2-y2

Q: 3. z = (c

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Q: Find the equation for the tangent plane to the surface z = - 9x - 7y at the point (2, 1, - 43). O A.…

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

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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: 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 an equation of the tangent plane to the surface 2² + 2y? + z? = 175 at the point (5, -5, 10).

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Q: Find the sum of the x-intercept, y-intercept, and z-intercept of any tangent plane to the surface…

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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: 17. Find the area of one side of the "winding wall" standing orthogonally on the curve x = y°, 0 < y…

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Q: The slope of the surface z = xy² in the x- direction at the point (2, 3) is O 12 O 8 O 1 O 9 O 10

A: The slope of the surface z = f(x,y) in the x-direction at (x0,y0) is given by [∂z/∂x](x0,y0) =…

Q: find an equation for the plane that is tangent tothe given surface at the given point. z = 4x2 + y2,…

A: It is given that, z = 4x2 + y2, at the point (1, 1, 5) We have to find the equation of tangent…

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

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Q: Find the equation of the tangent plane to the surface of the equation z = x2 + y2 - 2xy on the point…

A: Equation of tangent plane

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

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Q: Find the slope of the surface z = 3x/y at the point (5,2,15/2) in the x- and y- directions.

A: Given data is: z=3xy  To find the slope of the surface z at the point 5,2,152 in the x and…

Q: Find an equation of the plane tangent to the surface z2 - xy = 14 at (2, 1, 4).

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Q: Find the slopes of the surface in the x- and y-directions at the given point.

A: It is given that,z=xy  and point (1,2,2). We have to find the slopes of the surface in the x- and…

Q: Find the area of the portion of the surface x2 - 2z = 0 that lies above the triangle bounded by the…

A: Definition used:

Q: Sketch the section of the surface at y = 0. z = V4 +x² + y? 6 6 -8 -6 -4 -2 -2 -5-4-3--1, -8 -6 -4…

A: Given query is to the graph of the given expression.

Q: Find the equation of the tangent plane to the surface determined by a'y + z- 55 = 0 at a = 4, y = 3.…

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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: Sketch the section of the surface at y = 0. z = 6r 4 2 -6 -4 -2 6. -4- -6 6r 4 2 -6 -4 -2- -4 4. 2.…

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Q: The surface given by z = x² – y? is cut by the plane given by y = 3x, producing a curve in the…

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Q: Find the equation of the tangent plane and the normal line to the surface z=-2x -8y at the point…

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