Questions from General Calculus

Q: Let {pn} be a sequence of points determined as in

Let {pn} be a sequence of points determined as in the figure. Thus |AP1| = 1, |PnPn+1| = 2n-1, and angle APnPn+1 is a right angle. Find limn→∞∠Pn...

Q: Find the area of the shaded region. /

Find the area of the shaded region.

Q: To construct the snowflake curve, start with an equilateral triangle with

To construct the snowflake curve, start with an equilateral triangle with sides of length 1. Step 1 in the construction is to divide each side into three equal parts, construct an equilateral triangle...

Q: Find the sum of the series where the terms are the reciprocals

Find the sum of the series where the terms are the reciprocals of the positive integers whose only prime factors are 2s and 3s.

Q: Find the sum of the series ∑∞n=1 ln (

Find the sum of the series ∑∞n=1 ln (1 – 1/n2).

Q: Suppose you have a large supply of books, all the same

Suppose you have a large supply of books, all the same size, and you stack them at the edge of a table, with each book extending farther beyond the edge of the table than the one beneath it. Show that...

Q: Let Show that u3 + v3 + w3 - 3uvw = 1

Let Show that u3 + v3 + w3 - 3uvw = 1.

Q: If p > 1, evaluate the expression /

If p > 1, evaluate the expression

Q: Suppose that circles of equal diameter are packed tightly in rows inside

Suppose that circles of equal diameter are packed tightly in rows inside an equilateral triangle. (The figure illustrates the case n = 4.) If A is the area of the triangle and An is the total area occ...

Q: A sequence {an} is defined recursively by the equations

A sequence {an} is defined recursively by the equations