Display the values of the function in two ways (a) by sketching the surface z = f(x,y) and (b) by drawing an assortment of level curves in the function's domain f(x.y) = 12x + 3y? a. Choose the correct sketch of f(x.y) = 12x + 3y below O A. OB. OC. b. Choose the correct graph of the level curves below OB. OC. OA.

Q: Let f (z, y) = 4x+y. Find the slope of the surface z = point (1, -1). f (T, y) in the y-direction at…

A:

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 - 2xy + y²,…

A: Equation of tangent plane :  Fx(x-x0) + Fy(y-y0) -(z-z0) = 0

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² - 2xy + y²,…

A: Given that   f(x,y)= z = x2-2xy+y2     So,  this can be rearrange as…

Q: Display the values of the functions in two ways:(a) by sketching the surface z = ƒ(x, y) and (b) by…

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Q: Display the values of the function in two ways: (a) by sketching the surface z= f(x.y) and (b) by…

A: (a) Consider the given equation surface: f(x,y)=z=16y2  As, the equation represents a parabolic…

Q: Display the values of the function in two ways: (a) by sketching the surface z = f(x,y) and (b) by…

A: Given, f(x,y)= 24x²+6y²

Q: z=x¯-y¯ at (3,-2, 5)

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Q: Sketch a typical level surface for the function. 10) f(x, y, z) = /x2 –z %3D

A: sketch a typical level surface for the following 10) fx,y,z=x2-z it is known that level surface is…

Q: Find, to two decimal places, the areas of the surfaces generated byrevolving the curves about the…

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Q: Sketch a typical level surface for the function f(x,y,z) =2x² + y? +z?. Vhich of the following is a…

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Q: Q2: A. For the surface f derivative at (1,1 derivative and the line to the surface

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Q: Describe the level curves of: (a) f(x, y) = e4x-y (b) f(x, y) = In(4x – y) (c) f(x, y) = 3x² – 4y2…

A: (a) To decribe the  level curvesf(x, y)=e4x-y = 1 , 2 , 3, 4, 5

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 - 2xy + y²,…

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Q: Find the area of the surface generated when the given curve is revolved about the x-axis.  y =…

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Q: The area, in square units, bounded by the curves y = x² , y=2 – x and y=1 is ,

A: For a bounded figure, to find the area we need to determine the limits and the curves we need to…

Q: A surface has Cartesian equation :- f(xy). given by f(1.9)=6xy-5x -3y+ +7x-6y a) Use any…

A: To graph the function: z=f(x,y) where f(x,y)=6xy-5x2-3y4+7x-6y

Q: Describe the level surfaces for f (x, y, z) = y+10-√√x² + z² and sketch them for several (at least…

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Q: Display the values of the functions in two ways: (a) by sketching the surface z = ƒ(x, y) and (b) by…

A: Given function is: f(x,y)=4x2+9y2

Q: Display the values of the function in two ways: (a) by sketching the surface z = f(x,y) and (b) by…

A: Given the function is fx,y=9x2.

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² - 2xy + y²,…

A:

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² – 2xy + y²,…

A: Given problem:- Find an equation of the tangent plane to the surface at the given point. f(x, y) =…

Q: Given a surface f(x,y) = -2x² + (-3)y“. Find the derivative in the direction of v = at the point…

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Q: Given a function f(x, y) = V4 + 2x – 4y – x² – y². (i) Find the domain and range for the function f…

A: Given:                 fx,y=4+2x-4y-x2-y2 To do: Find the domain and range of fx,y. Sketch the…

Q: Display the values of the function in two ways: (a) by sketching the surface z= f(x,y) and (b) by…

A: solve for graph

Q: sketch a typical level surface for the function. ƒ(x, y, z) = ln (x2 + y2 + z2)

A: The given function is  ƒ(x, y, z) = ln (x2 + y2 + z2). In order to sketch the typical level surface…

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = L, (1,4, 4) 10 10

A: Equation of the tangent plane to the surface z=f(x,y) is                    r→.n→ =a→.n→; where…

Q: Given a surface f(x,y) = -3x² + (-4)y“. Find the derivative in the direction of v = at the point…

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Q: Given a surface f(x,y) = -2x² + (5)y². Find the derivative in the direction of v = at the point (7,…

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Q: Display the values of the function in two ways: (a) by sketching the surface z = f(x,y) and (b) by…

A: Given data÷ F(x,y)= 8x2+8y2 Now , we have to draw z=8x2+8y2

Q: Display the values of the function in two ways: (a) by sketching the surface z = f(x,y) and (b) by…

A: Consider the equation of surface f(x,y)=4y2 or we can write z=4y2 now we can see z is independent of…

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

A: Given: The function is fx,y=yx, 1,5,5. The objective is to find an equation of the tangent plane to…

Q: Find the area of the surface generated when the curve f(x) = (2/3)x^(3/2) - (1/2)x^(1/2) ; [1,9] is…

A: Given:

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = L, (1, 2, 2)

A: This is a problem of vector calculus.

Q: Display the values of the functions in two ways: (a) by sketching the surface z = ƒ(x, y) and (b) by…

A: Consider the given function f(x,y)=y2

Q: Display the values of the function f(x,y) = 1-ly| in two ways: (a) by sketching the surfacez =…

A: Here, we are given the function z=f(x, y)=1-|y|. For (a), We sketch the above surface by an online…

Q: Display the values of the function in two ways: (a) by sketching the surface z = f(x,y) and (b) by…

A:

Q: Given a surface f(x,y) = -3x² + (3)y². Find the derivative in the direction of v = at the point (5,…

A:

Q: If ƒ(x, y) = 100 ( y + 1) represents the population density of a planar region on Earth, where x and…

A: Given: The reginal population is f(x,y)=100(y+1) And the curve is f(x,y)=100(y+1)

Q: Find the plane tangent to the surface given by the function f(x, y) = (x² + y) sen(x - y) + 2x in…

A: Tangent plane  z= f(x0,y0)+fx (x-x0)+fy(y-y0)

Q: Display the values of the functions in two ways: (a) by sketching the surface z = ƒ(x, y) and (b) by…

A: Entering x and y values in the function will give us the exact plot of how the function goes. From…

Q: Display the values of the function in two ways: (a) by sketching the surface z= f(x,y) and (b) by…

A: Given fx,y=4x2+4y2

Q: 1. Sketch the graph of the level curves of the surface z = y + x^2 when k = −2, k = 0, and k = 2

A: Level curves problem.....

Q: Match the graph of the surface with one of the contour maps. f(x, y) = el=x*+y

A: Graph of given multivariable function is

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 – 2xy + y2,…

A:

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² – 2xy + y²,…

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

Q: Calculate the area of the surface generated when the curve, f(x) = x3/2 – on [1,2 ] is x'/2 revolved…

A: The surface area will be given by S=∫ab2πy1+dydx2dx

Q: Create a contour map of the surface by using the level curves for the following e values. z = 4x² +…

A: Level curves are defined are those curves which are formed when two planes get intersected. Here…