Questions from General Calculus

Q: (a). Graph the function. (b). Explain

(a). Graph the function. (b). Explain the shape of the graph by computing the limit as x→0 or as x→∞. (c). Estimate the maximum and minimum values and then use calculus to find the exact values. (d)....

Q: Ornithologists have determined that some species of birds tend to avoid flights

Ornithologists have determined that some species of birds tend to avoid flights over large bodies of water during daylight hours. It is believed that more energy is required to fly over water than ove...

Q: Find the dimensions of a rectangle with area whose perimeter is as

Find the dimensions of a rectangle with area whose perimeter is as small as possible.

Q: Investigate the family of curves given by f (x) =

Investigate the family of curves given by f (x) = xne-x, where n is a positive integer. What features do these curves have in common? How do they differ from one another? In particular, what happens t...

Q: The speeds of sound c1 in an upper layer and c2 in

The speeds of sound c1 in an upper layer and c2 in a lower layer of rock and the thickness h of the upper layer can be determined by seismic exploration if the speed of sound in the lower layer is gre...

Q: Two light sources of identical strength are placed 10 m apart.

Two light sources of identical strength are placed 10 m apart. An object is to be placed at a point P on a line l parallel to the line joining the light sources and at a distance meter from it (see th...

Q: Produce graphs of f that reveal all the important aspects of the

Produce graphs of f that reveal all the important aspects of the curve. Estimate the intervals of increase and decrease and intervals of concavity, and use calculus to find these intervals exactly....

Q: Sketch the graph by hand using asymptotes and intercepts, but not

Sketch the graph by hand using asymptotes and intercepts, but not derivatives. Then use your sketch as a guide to producing graphs (with a graphing device) that display the major features of the curve...

Q: If f' is the function considered in Example 3, use a

If f' is the function considered in Example 3, use a computer algebra system to calculate f' and then graph it to confirm that all the maximum and minimum values are as given in the example. Calculate...

Q: Describe how the graph of f varies as varies. Graph several

Describe how the graph of f varies as varies. Graph several members of the family to illustrate the trends that you discover. In particular, you should investigate how maximum and minimum points and i...