Find the volume of the region between the cylinder z = 2y² and the xy-plane that is bounded by the planes x = 0, x = 3, y = -3, and y = 3.

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A: Consider the following.To eliminate the parameter to find a Cartesian equation of the curve.

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Q: Suppose a product's revenue function is given by R(q) = -2q² + 700q, where R(q) is in dollars and q…

A: Revenue function is given by:Where, is in dollars is the units sold

Q: Evaluate the following integral, (9x - y²)dx + xy dy where C is given by x X = 5t, y = √t, 0 ≤ t s…

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Q: Exercise: 1) fx²e-3x dx 2) f x² Inxdx 3) sin3x cos4x dx

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A: To find the maximum and minimum values of f(x,y)=xy on the ellipse 5x^2+y^2=4, you can use the…

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Q: Find the area of the shaded region. y 3 2 1 (1, 1) 2 y = ³x y || 4 1 X 6 X = 8 CO 8 X

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Q: (b) Suppose that f(x) = 2x^2 − x^4 . Find the intervals on which f is increasing and those on which…

A: Question no. (b):Suppose that To find the intervals on which is increasing and those on which it is…

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A: To find all values of  such that  simutaneously.

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Q: 1) fx²e-3x dx/

A: Since you have asked multiple questions in a single request so we will be answering only first…

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A: f(t)=t−t3,[−1,4]