Questions from General Calculus

Q: There is considerable evidence to support the theory that for some species

There is considerable evidence to support the theory that for some species there is a minimum population m such that the species will become extinct if the size of the population falls below m. This c...

Q: Another model for a growth function for a limited population is given

Another model for a growth function for a limited population is given by the Gompertz function, which is a solution of the differential equation where c is a constant and M is the carrying capacity....

Q: In a seasonal-growth model, a periodic function of time

In a seasonal-growth model, a periodic function of time is introduced to account for seasonal variations in the rate of growth. Such variations could, for example, be caused by seasonal changes in the...

Q: Suppose we alter the differential equation in Exercise 19 as follows:

Suppose we alter the differential equation in Exercise 19 as follows: Exercise 19: In a seasonal-growth model, a periodic function of time is introduced to account for seasonal variations in the ra...

Q: The table gives the population of India, in millions, for

The table gives the population of India, in millions, for the second half of the 20th century. (a). Use the exponential model and the census figures for 1951 and 1961 to predict the population in 20...

Q: If f (x) =∑∞n=0 cnxn, where

If f (x) =∑∞n=0 cnxn, where cn+4 = cn for all n > 0, find the interval of convergence of the series and a formula for f (x).

Q: (a). What can you say about a solution of the

(a). What can you say about a solution of the equation y' = -y2 just by looking at the differential equation? (b). Verify that all members of the family y = 1/ (x + C) are solutions of the equation in...

Q: (a). What can you say about the graph of a

(a). What can you say about the graph of a solution of the equation y = xy3 when is close to 0? What if is large? (b). Verify that all members of the family y = (c – x2)-1/2 are solutions of the diffe...

Q: Solve the equation e-yy' + cos x = 0 and

Solve the equation e-yy' + cos x = 0 and graph several members of the family of solutions. How does the solution curve change as the constant C varies?

Q: Solve the initial-value problem y' = (sin x)/

Solve the initial-value problem y' = (sin x)/ sin y, y (0) = π/2, and graph the solution (if your CAS does implicit plots).