Questions from General Calculus

Q: What happens if you try to use l’Hospital’s Rule to evaluate Evaluate

What happens if you try to use l’Hospital’s Rule to evaluate Evaluate the limit using another method.

Q: Investigate the family of curves f (x) = ex -

Investigate the family of curves f (x) = ex - cx. In particular, find the limits as x→±∞ and determine the values of for which has an absolute minimum. What happens to the minimum points as increases?...

Q: Prove that for any positive integer n. This shows that the

Prove that for any positive integer n. This shows that the exponential function approaches infinity faster than any power of x.

Q: Prove that for any number p > 0. This shows that

Prove that for any number p > 0. This shows that the logarithmic function approaches ∞ more slowly than any power of x.

Q: If an initial amount A0 of money is invested at an interest

If an initial amount A0 of money is invested at an interest rate r compounded times a year, the value of the investment after t years is If we let n→∞, we refer t...

Q: If an object with mass m is dropped from rest, one

If an object with mass m is dropped from rest, one model for its speed after seconds, taking air resistance into account, is where g is the acceleration due to gravity and is a positive constant. (In...

Q: If an electrostatic field E acts on a liquid or a gaseous

If an electrostatic field E acts on a liquid or a gaseous polar dielectric, the net dipole moment P per unit volume is Show that lim E→0+ P (E) = 0.

Q: A metal cable has radius and is covered by insulation, so

A metal cable has radius and is covered by insulation, so that the distance from the center of the cable to the exterior of the insulation is R. The velocity v of an electrical impulse in the cable is...

Q: The first appearance in print of l’Hospital’s Rule was in the book

The first appearance in print of l’Hospital’s Rule was in the book Analyse des Infiniment Petits published by the Marquis de l’Hospital in 1696. T...

Q: Use a computer algebra system to graph f and to find f'

Use a computer algebra system to graph f and to find f' and f". Use graphs of these derivatives to estimate the intervals of increase and decrease, extreme values, intervals of concavity, and inflecti...