All problems refer to the following situation. The volume of water in a tank is

Question

All problems refer to the following situation. The volume of water in a tank is a function of time, V(t), with V in cubic inches and t in seconds. The rate of change of volume is given by dV/dt = 1.5 sin(2t) Write an integral for delta V on the time interval [0, t]. Do not evaluate your integral. You will be graded on the following elements: Correct integrand. Correct differential. Appropriate variable of integration. Correct limits of integration. Correct usage of integral notation. Several students guess formulas for V(t) Alice: guesses V(t) = 3 + 0.75 cos(2t) Write down the derivative of her guess. Simplify the derivative until you can decide if it is equal to 1.5sin(2t) Bob: guesses V(t) = 3 - 0.375 cos(2t) Write down the derivative of his guess. Simplify the derivative until you can decide if it is equal to 1.5sin(2t) Chris: guesses V(t) = 3 - 0.75cos(2t) Write down the derivative of this guess. Simplify the derivative until you can decide if it is equal to 1.5sin(2t) Dani: guesses V(t) = 3 + 3 cos(2t) Write down the derivative of this guess. Simplify the derivative until you can decide if it is equal to 1.5sin(2t) Which students guessed correct antiderivatives of 1.5 sin(2t)?

Explanation / Answer

All problems refer to the following situation. The volume of water in a tank is

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