Questions from General Calculus

Q: Verify that f (x) = sin 3√x is

Verify that f (x) = sin 3√x is an odd function and use that fact to show that

Q: Evaluate f2-2 (x + 3) √4 –

Evaluate f2-2 (x + 3) √4 – x2, dx by writing it as a sum of two integrals and interpreting one of those integrals in terms of an area.

Q: Use (a) the Midpoint Rule and (b) Simpson’s

Use (a) the Midpoint Rule and (b) Simpson’s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) Compare your results to...

Q: Evaluate f10 x√1 – x4, dx by making a

Evaluate f10 x√1 – x4, dx by making a substitution and interpreting the resulting integral in terms of an area.

Q: Which of the following areas are equal? Why?

Which of the following areas are equal? Why?

Q: A model for the basal metabolism rate, in kcal/h

A model for the basal metabolism rate, in kcal/h, of a young man is R (t) = 85 – 0.18 cos (πt/12), where t is the time in hours measured from 5:00 AM. What is the total basal metabolism of this man, f...

Q: If P (a, a2) is any point on the

If P (a, a2) is any point on the parabola y = x2, except for the origin, let Q be the point where the normal line intersects the parabola again. Show that the line segment PQ has the shortest possible...

Q: (a). If f (x) = ln x,

(a). If f (x) = ln x, 1 < x < 4, use the commands discussed in Exercise 9 to find the left and right sums for n = 10, 30, and 50. Exercise 9: Some computer algebra systems have commands that will dr...

Q: A manufacturer of lightbulbs wants to produce bulbs that last about 700

A manufacturer of lightbulbs wants to produce bulbs that last about 700 hours but, of course, some bulbs burn out faster than others. Let F (t) be the fraction of the company’s bulbs...

Q: An oil storage tank ruptures at time t = 0 and oil

An oil storage tank ruptures at time t = 0 and oil leaks from the tank at a rate of r (t) = 100e-0.01t liters per minute. How much oil leaks out during the first hour?