Given w = f(x, y, z) = 4r + y + 4z². Sketch the level surface of the function for w = 1.

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…

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Q: Find an equation for the plane that is tangent to the surface z=ln(x2+y) at the point P(0,1,0).

A: we have to find the equation of the tangent plane

Q: Given z = f(x, y) = V² + y² + 4y. (a) Find its domain and range. (b) Sketch the level curves for z =…

A: Introduction: Assume D is a subset of R2. A rule that assigns each pair (x,y) in D a value z=f(x,y)…

Q: find an equation for the plane that is tangent tothe given surface at the given point.11. z = ln (x2…

A: To find an equation for the plane that is tangent to the given surface at the given point. Given…

Q: f(x, y, z) = x² + 3y² + 5z?

A: Let us assume f(x,y,z)=x2+3y2+5z2=k Assume that k≠0 x2+3y2+5z2=k Divide both sides by k,…

Q: What is the equation of the surface revolved about the x-axis for z² - xz = ln x + 3x? A. y² + z² =…

A: Given: The equation of surface which is z2-xz=lnx+3x. This equation is a quadratic equation for z.…

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: 2. For the surface z = In(y+ Vx² + y²). (a) Find an equation of the tangent plane at the point (3,…

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Q: Find the equation of the tangent plane to the surface z = e17 In(1y) at the point (-3, 1,0). Note:…

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Q: Q4) given the surface: cos nx – x²y + exz + 2yz = 2 Find the equation of the tangent plane and…

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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: At which of the points below is the tangent plane to the surface x² – 2y + z + yz = 2 vertical?…

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Q: For f(x, y, z) = x^2 − 6x + y^2 + z^2 , describe and draw the level surface for the function value…

A: Let w=f(x,y,z) . The level surfaces of w=f(x,y,z) results, when w=k slices the the function,…

Q: Let f(x, y, z) = xyz + 3. Find an equation of the level surface that passes through the point (a)…

A: Given: fx,y,z=xyz+3 Let fx,y,z=xyz+3 the level surface are given by, xyz+3=k        ,k∈ℝ…

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: The level surface of f(x, y, z)=Vx²+y² -5_of height 2 is O a. A circle of radius /2 O b. A cylinder…

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Q: Find the center of mass of the thin plate bounded by the y-axis and the lines y =x and y = 2 - x…

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Q: Find a formula for a functionf(x, y, z) whose level surface f= 3 is a cylinder of radius 5 centered…

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Q: et f(z, y) = for (z, y) # (0,0). Find the level curves of 2 + y²

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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: Find the angle of inclination of the tangent plane to the surface x2+ y2+ z2 = 14 at the given point…

A: Consider the function fx,y,z=x2+y2+z2-14. Gradient of f can be obtained as follows. ∇fx,y,z=∂∂x,…

Q: a) Consider the surface f(x, y) = x-y+1. (i) Sketch the level curves of height C=0 and C=4 for 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: If ƒ(x, y) = 100 ( y + 1) represents the population density of a planar region on Earth, where x and…

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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: ) Find the gavea d the rgion enclased by the line x-In3 and the curves y= ex and y=ex

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Q: find the surface area of the portion of the curve x²+y²=4 from x=0 to x=2 when it is revolved about…

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

A: Follow the procedure given below.

Q: What kind of surfaces are the level surfaces f(x, y, z) = const? 9. f = 4x – 3y + 2z 11. f = 5x² +…

A: (13) Given  f=z-(x2+y2)     Level surfaces ,   f(x,y,z)=C   (constant) i.e z-(x2+y2)=C i.e…

Q: Given z = f(x, y) = Va2 + y² + 4y. %3D (a) Find its domain and range. (b) Sketch the level curves…

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Q: Let f(x, y, z) = x^2 - y^2 – z. Describe the level surfaces.

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Q: Given w = f (x, y, z) = 4.x² + y² + 4z². Sketch the level surface of the function for w = 1.

A: We have to sketch the level surface of the following function for w=1, w=f(x,y,z)=4x2+y2+4z2

Q: The area of the surface obtained by rotating the curve y = √√x + 1, for 0 ≤ x ≤ 2, about the x-axis,…

A: Given :

Q: (b)Let f(x, y) = / 3x + 2y. Find the slope of the surface z f(x, y) in the x-direction at the point…

A: Slope of z= f(x, y) in the y- direction at the point (4,2) Slope of in the y - direction means…

Q: What kind of surfaces are the level surfaces f(x, y, z) = %3D const? 9. f = 4x – 3y + 2z 10. f =…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 3 For the curve y =÷ (x² + 1)z, find the following requirements over the interval 2 < x< 3: 1. The…

A: First differentiate wrt x and  then use formula of length of curve

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

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Q: Sketch a typical level surface for the function f(x,y,z) = z - 2x2 – y?. Choose the correct answer…

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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: Given w = f(x, y, z) = 4x2 + y? + 422. Sketch the level surface of the function for w = 1. %3D 2.

A: Given that: w=f(x, y, z)=4x2+y2+4z2

Q: If f(x, y, z) = V3x + y2 – 2z, then find the slope of the surface f in the x- direction at the point…

A: We are given a surface: f(x,y,z) = 3x+y2-2zWe need to find the slope of surface f in the x-direction…

Q: If 0 ≤ f (x) ≤ g(x) for x in the interval [a, b], can the surface obtained by rotating the graph of…

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Q: Find the surface area of the rotating object from the curve y = x^2 with the constraint 0 ≤ x ≤ 1…

A: The formula for the surface area of the rotating object from the curve y=f(x) with the constraint…

Q: Find the surface area of the rotating object from the curve y = x^2 with the constraint 0< x <1…

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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 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: Let f (x, y) = 4x° + y°. Find the slope of the surface z = f (7, y) in the y-direction at the point…

A: The given problem is to find the slope of the given surface in y-direction at the point (1,-1).

Q: (b)Let f(x, y) = /3x +2y. Find the slope of the surface z = f(x,y) in the x-direction at the point…

A: It is given that, f(x,y)=3x+2y. It is known that the slope of any function is defined as,…

Q: Below is a curve C, which is the intersection between the surfaces  S1 : z = 4 − x2 S2 : z + 2x −…

A: Given that,Below is a curve C, which is the intersection between the surfaces   S1 : z=4−x2  S2 :…

Q: nd the minimum distance from the point to the surface z = V7- 2x - (-2, -2, 0)

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