Questions from General Calculus

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 is measured in seconds and the units for r (t...

Q: (a). If f (x) = sin (sin

(a). If f (x) = sin (sin x), use a graph to find an upper bound for f(4) (x). (b). Use Simpson’s Rule with n = 10 to approximate fπ0f (x) dx and use part (a) to estimate the error. (c). How large shou...

Q: The marginal cost of manufacturing x yards of a certain fabric is

The marginal cost of manufacturing x yards of a certain fabric is C'(x) = 3 – 0.01x + 0.000006x2 (in dollars per yard). Find the increase in cost if the production level is raised from 2000 yards to 4...

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,...

Q: In the figure, the length of the chord AB is 4

In the figure, the length of the chord AB is 4 cm and the length of the arc AB is 5 cm. Find the central angle θ, in radians, correct to four decimal places. Then give the answer to the n...

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

Q: A car dealer sells a new car for $18000. He

A car dealer sells a new car for $18000. He also offers to sell the same car for payments of $375 per month for five years. What monthly interest rate is this dealer charging? To solve this problem, y...

Q: (a) Show that 1 < √1 + x3 <

(a) Show that 1 < √1 + x3 < 1 + x3 for x > 0. (a) Show that 1 < f10 √1 + x3 dx < 1.25.

Q: (a). Show that for cos (x2) > cos

(a). Show that for cos (x2) > cos x for 0 < x < 1. (b). Deduce that for fπ/60 cos (x2) dx > 1/2.

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.