Questions from General Calculus

Q: One method of slowing the growth of an insect population without using

One method of slowing the growth of an insect population without using pesticides is to introduce into the population a number of sterile males that mate with fertile females but produce no offspring....

Q: Factor x4 + 1 as a difference of squares by first adding

Factor x4 + 1 as a difference of squares by first adding and subtracting the same quantity. Use this factorization to evaluate /

Q: (a) Use a computer algebra system to find the partial

(a) Use a computer algebra system to find the partial fraction decomposition of the function (b) Use part (a) to find / (by hand) and compare with the result of using the CAS to integrate f directly....

Q: (a) Find the partial fraction decomposition of the function

(a) Find the partial fraction decomposition of the function (b) Use part (a) to find / and graph f and its indefinite integral on the same screen. (c) Use the graph of f to discover the main features...

Q: (a) Use integration by parts to show that, for

(a) Use integration by parts to show that, for any positive integer n (b) Use part (a) to evaluate

Q: Suppose that F, G, and Q are polynomials and

Suppose that F, G, and Q are polynomials and for all x except when Q(x) = 0. Prove that F(x) = G(x) for all x.

Q: If f is a quadratic function such that f(0)

If f is a quadratic function such that f(0) = 1 and is a rational function, find the value of f(0).

Q: If a ≠ 0 and n is a positive integer, find

If a ≠ 0 and n is a positive integer, find the partial fraction decomposition of

Q: Evaluate the integral using the indicated trigonometric substitution. Sketch and label

Evaluate the integral using the indicated trigonometric substitution. Sketch and label the associated right triangle.

Q: Evaluate the integral using the indicated trigonometric substitution. Sketch and label

Evaluate the integral using the indicated trigonometric substitution. Sketch and label the associated right triangle.