Questions from General Calculus

Q: Water flows from the bottom of a storage tank at a rate

Water flows from the bottom of a storage tank at a rate of r(t) = 200 - 4t liters per minute, where 0 ≤ t ≤ 50. Find the amount of water that flows from the tank during the first 10 minutes.

Q: (a) If f (x) = ex cos x

(a) If f (x) = ex cos x, find f ‘(x) an) f ‘’(x). (b) Check to see that your answers to part (a) are reasonable by graphing f , f ‘, and f ‘’.

Q: The velocity of a car was read from its speedometer at 10

The velocity of a car was read from its speedometer at 10-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car.

Q: Find dy/dx by implicit differentiation. ex/y

Find dy/dx by implicit differentiation. ex/y = x - y

Q: If H(θ) =  θ sin θ ,

If H(θ) =  θ sin θ , find H’(θ) and H’’(θ).

Q: Suppose that a volcano is erupting and readings of the rate r

Suppose that a volcano is erupting and readings of the rate r(t) at which solid materials are spewed into the atmosphere are given in the table. The time t is measured in seconds and the units for r(t...

Q: If f (t) = sec t, find f’’ (

If f (t) = sec t, find f’’ (π/4).

Q: (a) Use the Quotient Rule to differentiate the function

(a) Use the Quotient Rule to differentiate the function f (x) = tan x – 1 / sec x (b) Simplify the expression for f (x) by writing it in terms of sin x and cos x, and then find f ‘(x). (c) Show that y...

Q: Water flows into and out of a storage tank. A graph

Water flows into and out of a storage tank. A graph of the rate of change r(t) of the volume of water in the tank, in liters per day, is shown. If the amount of water in the tank at time t = 0 is 25,0...

Q: Suppose f (π/3) = 4 and f ‘(

Suppose f (π/3) = 4 and f ‘(π/3) = 22, and let g(x)d = f (x) sin x and h(x) = (cos x)/f (x). Find (a) g’(π/3) (b) h’(π/3)