If z = f (x, y) is a smooth continuous surface such that f.(a,b) =0 and f,(a,b) =0 then what can you say about the tangent plane, normal line, and the behavior of the surface at the point (a,b, f(a,b))? Use complete sentences please.

Q: Consider the surface O3z+3y-2z=0 O 34z + 7y-12z = 0 O 3x+3y-2z=147 What is the equation of the…

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Q: 2) Draw contour maps for functions f(x, y) = x² - 4y², and g(x, y) = x² + 4y². What shape. are these…

A: The contour of function f(x,y) represents parabolas.

Q: The surface z = x² - y² and the surface ryz = -30 intersect along a curve in R³. Find a vector…

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Q: (10) Let f(x, y) = /x-y a) Find the domain and range of f (x, y). Sketch the domain on the x-y…

A: Step:-1 Given that fx, y =x-y Part (a):- The square root function is real when x-y≥0 x-y≥0⇒x≥y⇒y≤x…

Q: Match the graph of the surface with one of the contour maps. /x, y) = el-x+y

A: By using graphing plotter, (x,y,z)=(x,y,f(x,y)).

Q: Find the lines curvatures, the first and second fundamental forms of the surface: the surface

A: As per the question we are given a surface. And we have to find its first and second fundamental…

Q: f(x,y)=9-x^2- y^2

A: We have to find standard form of the given equation and then identify the surface

Q: The equation z = f(x,y) = y +x -3y defines a surface. What is t- equation of the tangent plane at…

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Q: Which of the following is the coordinates of all points on the surface with equation z = x³-5xy¹…

A: To find the coordinates of all points on the surface where the surface has a horizontal plane, we…

Q: Please carefully find the domain of the function f(x, y, z) = as a familiar surface. 4x²+92²-25y and…

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Q: Describe and draw at least 3 level surfaces for the function f(r, y, z) = x²+ y? - z?

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Q: Consider the function f(x, y, z) = 3x² + y² - 4z. i) A contour surface S passes through the point A…

A: To find the value of the contour surface passing through the point A = (2, 3, -1), we need to…

Q: Describe and sketch the surface given by the function.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: a) Mark the points on the contours where Iz = 0. b 2.

A: A contour line or level curve is the intersection of a surface with a horizontal plane. For example…

Q: 4. Find an equation of the tangent plane to the surface z = xy+8 xy-2x at the point (1,1,–10)

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Q: Discribe the topology through diagrams of surface and curves

A: Describe topology through diagrams of surface and curves.

Q: Consider the surface What is the equation of the tangent plane to the surface at the point…

A: Given surface is -2x3-2xy+2xyz=36 The equations of the tangent plane and the line normal to the…

Q: 2) Given f(x,y) Dand some domain, vertica) traces, horizontal traces then gruph the surface. 10…

A: Given Data: Let us consider the given function is, fx,y=101+x2+y2. To Find: Domain, vertical…

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 the directional derivative of f(x,y,z)=xe +ye² at (0,0,0) in the direction of the vector…

A: As per our guidelines, I can answer only one question. To know rest please re upload particular…

Q: Sketch the surface of f(x,y)

A: To sketch the function