Questions from General Calculus

Q: Make a substitution to express the integrand as a rational function and

Make a substitution to express the integrand as a rational function and then evaluate the integral.

Q: Use a graph of f (x) = 1/ (

Use a graph of f (x) = 1/ (x2 – 2x – 3) to decide whether f20 f (x) dx is positive or negative. Use the graph to give a rough estimate of the value of the integral and then use partial fractions to fi...

Q: Write out the form of the partial fraction decomposition of the function

Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients.

Q: Graph both y = 1/ (x3 – 2x2) and

Graph both y = 1/ (x3 – 2x2) and an antiderivative on the same screen.

Q: (a). Show that the area of a triangle with sides

(a). Show that the area of a triangle with sides of lengths a and b and with included angle θ is A = 1/2 ab sin θ (b). Find the area of triangle ABC, correct to five decimal...

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: The region under the curve y = 1/x2 + 3x

The region under the curve y = 1/x2 + 3x + 2 from x = 0 to x = 1 is rotated about the x-axis. Find the volume of the resulting solid.

Q: Find the limit. limn→∞ ∑n i=1

Find the limit. limn→∞ ∑n i=1 1/n (i/n)2

Q: Find the limit. limn→∞ ∑n i=1

Find the limit. limn→∞ ∑n i=1 1/n [ (i/n)3 + 1]

Q: Find the limit. limn→∞ ∑n i=1

Find the limit. limn→∞ ∑n i=1 2/n [ (2i/n)3 + 5 (2i/n)]