Questions from General Calculus

Q: Now try b = 1 and a = n/d,

Now try b = 1 and a = n/d, a fraction where n and d have no common factor. First let n = 1 and try to determine graphically the effect of the denominator d on the shape of the graph. Then let n vary w...

Q: First make a substitution and then use integration by parts to evaluate

First make a substitution and then use integration by parts to evaluate the integral.

Q: Evaluate the integral. /

Evaluate the integral.

Q: If the circle C rolls on the outside of the fixed circle

If the circle C rolls on the outside of the fixed circle, the curve traced out by P is called an epicycloid. Find parametric equations for the epicycloid.

Q: Find the Maclaurin series of f (by any method) and

Find the Maclaurin series of f (by any method) and its radius of convergence. Graph f and its first few Taylor polynomials on the same screen. What do you notice about the relationship between these p...

Q: Show that the area of R is /

Show that the area of R is

Q: Find the area of the region shown in the figure below.

Find the area of the region shown in the figure below.

Q: Find a formula (similar to the one in Problem 1)

Find a formula (similar to the one in Problem 1) for the volume of the solid obtained by rotating 5 about the line y = mx + b. Data from Problem 1: Show that the area of / is

Q: Find the volume of the solid obtained by rotating the region of

Find the volume of the solid obtained by rotating the region of Problem 2 about the line y = x - 2. Data from Problem 2: Find the area of the region shown in the figure below.

Q: Use a computer algebra system to find the exact area of the

Use a computer algebra system to find the exact area of the surface obtained by rotating the curve / Then approximate your result to three decimal places.