When does a series converge?

Does the harmonic series converge?

Can you find another series which seems like it should converge

, but it diverges?

Does the alternating harmonic series converge?

a. The plane x = 2 is

b. Which of the following vectors is not perpendicular to vector u =(-5, 2, 1)?

c.Given unit vectors i, j and k, 2j × 3k=

d. If Car A is travelling north at 50 km/h and Car B is travelling south at 60 km/h, the velocity of Car A relative to Car B is

e. Given three vectors, u, v, and w, if u • (v × w) = 0, what geometrical result can be concluded?

f. The plane (x, y, z) = (4, 2, 1) + s(1, 1, -2) + t(2, -1, 3), converted into scalar form, has equation

Three students answer a true-false question on a test randomly. A random variable x represents the number of answers of true among the three students, taking on the value 0, 1, 2, or 3.

(a) Find the frequency distribution for x.
(b) Find the probability distribution for x.

For the same random variable x as the previous problem, find the following:

(a) The expected value (b) The variance (c) The standard deviation

2.a Use Rolle's Theorem to prove that if f ′ ( x ) = 0 for all xin an interval ( a , b ), then f is constant on ( a , b ).

b True or False. The product of two increasing functions is increasing. Clarify your answer.

c Find the point on the graph of f ( x ) = 4 − x 2 that is closest to the point ( 0 , 1 ).

An open-top box is to be made from a 20cm by 30cm piece of cardboard by removing a square from each corner of the box and folding up the flaps on each side. What size square should be cut out of each corner to get a box with the maximum volume?

Given the geometric sequence an = 4n . Find the first three terms and the common ratio.

The business manager of a 90 unit apartment building is trying to determine the rent to be charged. From past experience with similar buildings, when rent is set at $400, all the units are full. For every $20 increase in rent, one additional unit remains vacant. What rent should be charged for maximum total revenue? What is that maximum total revenue? To help solve the above scenario, perform an internet search for Profit Parabola or Applications of Quadratic Functions. List the URL of one of the applications that you find. URL ___________________________________________________________________

Go to http://www.purplemath.com/modules/quadprob3.htm to see the process used for determining the quadratic function for revenues R(x) as a function of price hikes x on page 3 with the canoe-rental business problem. Use this process to determine the quadratic function that models the revenues R(x) as a function of price hikes x in the apartment building scenario above. 

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. y = 2 + 2 sqrt(x) , y = (6 + x) / 3

Suppose that the batting averages in baseball are normally distributed so that the mean is .258 and the standard deviation is 0.04. What is the probability that a player has a batting average of

(A) More than .258?

(B) More than .298?

(C) More than .318?

Determine if ∑(-1)^n/(4n-7), n=0 to infinity, absolutely or conditionally converges or diverges?

Find value of a6 of the Tayler series found by a0, a1x, a2x^2+...