Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on the right 7 by the graph of g(y) = and on the left by the y-axis for 1 ≤ y ≤ 12, about the x-axis. Round your y answer to the nearest hundredth position.

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A: Application of Derivative

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Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) = 3x² +…

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Q: Consider the ellipse 9x² + 64y² = 576. Consider the point P(16,3). Find an equation for both lines…

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Q: -4 +00 24 y 2 -20 -2 4 2 4 ४ c. 1

A: we will find the required.

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Q: 12. The average rate of change of f(x) = (x-a)² over the interval a ≤ x ≤a + 1 is

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Q: Find the absolute extrema of the function, if they exist, over the indicated interval. Also indicate…

A: Given function is:fx=-0.001x2+4.2x-80We have to find the absolute extrema of the function.

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Q: Solve Ч 3ху= 4'=45х +уз

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Q: Consider the curve 1x² - - 2xy 1y³4.25. (a) Find an expression for y'. y' = (b) P(-1.5, 1) is on…

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Q: Use polar coordinates to find the volume of the given solid. bounded by the paraboloids z = 10 - x²…

A: The solution is shown below-

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Q: -S X √196+x -dx =

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Q: Let f(x) = 7x sin(x) cos(x). Evaluate f'(x) at x = ³7. ƒ'( ³ ) =

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Q: How do you find the absolute max and min for problem 45?

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Q: In this problem, p is in dollars and q is the number of units. (a) Find the elasticity of the demand…

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Q: Verify that the two planes are parallel, and find the distance between the planes. (Round your…

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Q: The function f(x) = 1 + 8x + 128x7 has one local minimum and one local maximum. This function has a…

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Q: (b) g(x) = (x + e*)², [0, In 4]

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Q: Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and…

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Q: Consider the following. f(x, y) = 9x y A /2 sin(0) 1/2 ([ 0 r = sin 0 (a) Set up an iterated…

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Q: Find the average value of f(x,y) = sin (x + y) over 0≤x≤/3, 0≤ y ≤5/3 0 ≤x≤2/3,0 ≤ y ≤7π/6 a. the…

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Q: Solve the differential equation. 2xy + 4x + (x² - 4) dy = 0 dx

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Q: The Fifth Gate After traversing your continuous path, you finally arrive at Gate 5. Your computer…

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Q: Calculate the derivative of the function. HINT [See Example 3.] h(x) = 3[(6x − 1)(x − 1)]−1/3

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