Let S be the surface with equation (z - 4)² = 4x² + 4y². Viewing S as a surface of revolution, find an equation of a generating curve on the yz-plane and determine its corresponding axis of revolution. Hint: This is a cone.

Q: Solve for the Partial Derivatives and total differential of each of the following function

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Q: Find the area bounded by the parabolas (x-3)² - 16ky = 0 and y² - 16k (x-3) = 0.

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Q: Solve y at x=1. dy/dx - 2(x+1)^3 = 4y/(x+1)

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Q: 27 3. Explain how you would find the general term of the sequence: 4, -6, 9, - ".

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Q: ds Find the complete solution of = 8t³ √s. dt

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Q: 1. u= x² + y² + z²

A: On solving this we will get

Q: 2. a+b+c=c+b+a is true because of

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Q: 5. Calculate the sum of the first 23 terms of the sequence defined below. tn 10+ 3n, n E N

A: We have to find the sum

Q: Find the volume of the solid generated by the region bounded by y - x² = -3, x+y = 3 about y = -5.

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Q: Find the area bounded by the parabolas (x - 1)² = 4ay and y² + 4a = 4ax.

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Q: Find the acute angle between two tangent lines at point of intersection between two curves xy = 5…

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Q: then what is y at x=1?

A: We can find y at x=1 in the following steps.

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A: Let the radius of the cylinder is = r and the radius of the sphere = R  Let the height of the…

Q: Determine the center-radius Form of the equation of the sphere whose diameter has endpoints at (2,…

A: The first question has been solved as per the request of the student.     The center radius form of…

Q: Find Vector A and B such that A is parallel to , B is perpendicular to and A + B =

A: We have to find vectors A and B such that A is parallel to 2, 1,-1, B is perpendicular to 2, 1,-1…

Q: A product can be produced at a total cost of C(x) = 500 + 100x² + x³ dollars, where x is the number…

A: Solved below.

Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answer. 1 S₁° 19 dx…

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Q: Find the Area of the Surface obtained by rotating the curve about the x-axis y = cosh x, 0≤x≤1

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Q: Determine the center-radius Form of the equation of the sphere whose- diameter has endpoints at (2,…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: = Find the area bounded by the curves -x + y² = 8, x = -2y and y

A: Follow the procedure given below.

Q: Show that the three functions: f₁(x) = ex-8,f₂(x) = ex, f(x) = 4(2x-2) are linearly dependent.

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Q: 5. x x2 + x − 6 dx

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Q: Determine if the function f (x, y) = if (x, y) = (0,0) is continuous at (x, y) = (0,0). If not,…

A: Use limit to find wheather function is continuous or discontinuous.

Q: Given x - ³²+2y — In(y + 1), find the arc length for 0 ≤ y ≤4 8

A: The arc length of the curve x=f(y) for a≤y≤b is given by ∫ab1+dxdy2 dy

Q: TYPEWRITTEN

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Q: The volume of a cube is increasing at the rate of 4cm³/min. How fast is the surface area increasing…

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A: Here we have to find the equation of the tangent line of the function…

Q: Solve the first order linear ordinary differential equation x sin x dy dx + (sin x + x cos x) y =…

A: Here, the given DE can be written as: xsin xdydx+(sin x+x cos x)y=xex⇒dydx+sin x+x cos xxsin…

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Q: Solve ₂(x + 1)(x + 2)²(x²-1)dx with and without the even-odd theorems (show both solutions).

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Q: Find the height of a circular cylinder of max. volume that can be cut from a spherical wood of…

A: using double derivative test to find out height when cylinder volume would be maximum.

Q: Question

A: Please refer to the image below

Q: Given x = - ³²+2y — In(y + 1), find the arc length for 0 ≤ y ≤ 3 8

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Q: Consider the vector-valued function R(t) = (t³-t, 2t², 2 - 21²). 1. Find ||'(t)||. (Simplify your…

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Q: If f(x) = 10, find f'(-1).

A: Given f(x)=10,  to find f'(-1) Formula used Differentiation of a constant value is zero d (constant)…

Q: · ƒ³3(x + 1)(x + 2)²(x² −1)dx with and without the even-odd theorems (show both solutions).

A: Solution :Without odd-even…

Q: In x Compute -dx. 3√√/x 9 X 3 A²x²0 nx-x²²+ C A.- In 2/3 2 4 1 B.- - +C X 3 4/3 4 3 C.--(In x)x-4/3…

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Q: A product can be produced at a total cost of C'(x) = 500 + 100x2 + x³ dollars, where x is the number…

A: Given that; Cost function and revenue function.

Q: Find arc length for the curve (y+1)2=4x3 x=0 ,x=1

A: This question can be solved using the concept of length of arc of a given curve over a given…

Q: ds π Find a particular solution of =10csc² 2t determined by s= 2 when t == . — = dt

A: Given:ds/dt=10csc^2(2t) To find: solution at s=2 and t=π/4

Q: Find the area bounded by y³ = x² and x-axis, from x = 0 to x = 8.

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Q: the particular solution

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Q: Evaluation. 1. Determine the antiderivative for each. Show complete solution. √ 5x³=3 dx 2. √(√x√x +…

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Q: What are the domain and range of f(x)= In x? A. The domain and range are both all positive real…

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Q: (b) The function y(x) satisfies the inhomogeneous second order linear differential equation d²y dy +…

A: We have to find the general solution of the given differential equation using variation of…

Q: 3 N -3 -2 -1 1 2 3 1 . For the above function f(x) = 2 1.2, estimate f'(x) using h = 0.001 for the…

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