Consider a solid bounded by, x² + y²=16, z=y², z=0 and x=0 Calculate its volume.

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Q: b) Show that the ode (x + tan-¹ y) dx + x+y dy = 0 is exact, then find the general solution and 1+y²…

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Q: Let the function f: R→ R be defined by f(x) = { Question 1 0, x2, x=0, x = 0. (a) Explain the…

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Q: 5. Let f(x, y, z) = -k x²+y²+z² with k a constant. A. Calculate the maximum rate of increase of f(x,…

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Q: Verify that the pair x(t) = e 20t, y(t) = e 4t is a solution to the given system below. Sketch the…

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Q: a. 1 L₁cos .x³dx

A: As per the Bartleby guidelines I am answering only first question. Kindly upload again and clearly…