What is the equation of the surface revolved about the x-axis for z² - xz = ln x + 3x? A. y² + z² = Inx+3x+xz x² 1 ---------| In x + 3x + B. y² + z² C. y² + z² x² In x + 3x + 4 1 D. y² + z² = lnx + 3x + x(lnx + 3x)

Q: Evaluate fay'da + aªdy, where C is the rectangle with vertices (0,0), (1,0), (1,4), and (0,4)

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Q: Identify the surface for z=r^

A: Given z=r2

Q: Find the equation of the circle which is touched by y = x has on the positive direction of the x -…

A: Since the required circle has its center on the x-axis,let the coordinates of the center be…

Q: Find the equation of the tangent plane to th surface 3x? + 5y? + 4z2 = 24 at the point (1, –1,2). 1.…

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Q: Let C be the upper half of the circle of radius 3 centered at (0, 0). Let f (x, y) be the square of…

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Q: Find the point(s) on the surface z^2=xy+1 which are closest to the point (10,11,0).

A: We have to find the the point(s) on the surface z^2=xy+1 which are closest to the point (10,11,0).

Q: 4. Determine the slope of the common tangent to the parabolas y=x² +1 and y=-x² - 1. y=x*2+1 (a, b)…

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Q: SF. dr, where F (x, y) = (6x − 2y)i +x²7, Evaluate from (6,-3) to (0, 0). and C is the line segment

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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: Q3: Find the points on the surface x^2+z^2-630, closest to the origin.

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Q: Suppose that the plane tangent to the surface z = f(x, y) at (-4, 2, 5) has equation z + 5x + 4y =…

A: From the equation of tangent, we can derive: z = -(7 + 5x + 4y) Hence,

Q: na the General Form of thE circi (x+5)^2+(y-1)^2=9 *

A: Given equation is x+52+y-12=9Write the general form of the circle

Q: a) Determine the point at which the slope of the tangent to each parabola is zero. i) y= 6x2-3x + 4…

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Q: 2) Describe the level curves of the surface Z = √36 4X² 9Y²

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Q: Can the level surface x^2 + y^2 + z^2 − 5 = 0 be expressed as the graph of a function f(x, y)?

A: Level surface isif possible then we have to express as it the graph of a function f(x, y).

Q: A rectangular plate with an area of 36 cm? is to be produced on a lathe in such a way that the…

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Q: Two circles have equations of x2 + y2 – 4x – 4y + 4 = 0 and x2 + y2 – 4x + 8y + 4 = 0. Compute the…

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Q: Show that the distance between the line 3x 4y + 3 = 0 and the point (1, –1) is 2. |

A: In this question, we have to prove that the distance between line and point is 2.

Q: Q1.6 Find the point on the surface given by the equation x^2 + 5y^2 + 10z^2 = 18016 that has a…

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Q: Q3: Find the points on the surface x^2+z^2-6=0, closest to the origin.

A: Given: x2+z2-6=0 Let x,y,z be the point on surface x2+z2-6=0 which is closet to point 0,0,0 Then the…

Q: Ass: 一 V EXAMPLE 6 Find the area enclosed by the line y = x - 1 and the parabola y² = 2x + 6.

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Q: Double integrate under the hyperbolic paraboloid z=x2-y2 on the triangular footprint made by the x…

A: In the given question we have to find the double integral of paraboloid z=x2-y2 ovet the triangle…