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Q: ty′+(t+1)y=t,y(ln 2)=1,t>0

A: Consider the provided first order differential equation with initial condition,

Q: Use Pappus’s Theorem for surface area and the fact that the sur-face area of a sphere of radius a is...

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Q: dy/dx of y=e^3x+1

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Q: consider the equation f(x) = 2x2 - x Find the net change between x = 3 and x = 6

A: To determine the net change of the function on the given interval.

Q: The autonomous differential equations in Exercises 9–12 represent models for population growth. For ...

A: Consider the provided autonomous differential equation,

Q: 2y′ + y = 3t2

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Q: A thin plate of constant density d = 1 occupies the region enclosed by the curve y = 36/(2x + 3) and...

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Q: What is the law of exponential change? How can it be derived from an initial value problem? What are...

A: To define the law of exponential change and derive it from initial value problem.

Q: A brief calculation shows that if 0<=x<= 1, then the second de-rivative of ƒ(x) = sqrt(1 + x4)...

A: The Given information is,