Cantor Sets

1. Show that the Cantor function c: [0, 1]  [0, 1] is continuous. To do this, I know I need to use the fact that c is monotone, but I’m having difficulty from there. 2. Compute ∫c, where c is considered to be an element of L+(R). (let c(x) =0 for x not in [0, 1]) Here, c is the Cantor Function and L+(R ...continues

Infinite Series : Convergent Series of Nonnegative Terms

1. Show that if the infinite sum ∑∞ xn is a convergent series of non-negative terms, must ∑∞√xnxn+1 be convergent? Prove or give a counterexample. 2. Find the value of ∑∞n=2 ln(1-1/n2).

Math Analogies

1. In a percent change graph of an average teachers annual salary the bars representing successive years are either unchanged or decreasing in size. 2. Consider a typical 30 year fixed rate mortgage. During the first few years of the loan are payments applied primarily towards interest or primarily towards principal? Explain ...continues

Effects on break even points.

Would each of the following increase, decrease, or have an indeterminant effect on a firm’s breakeven point (unit sales)? a. An increase in the sales price with no change in unit costs. b. An increase in fixed costs accompanied by a decrease in variable costs. c. A new firm decides to use MACRS depreciation for both book a ...continues

Which of the following lists correctly ranks investments from highest to lowest returns and risk (thus, the highest risk security should be shown first, the lowest risk securities shown last)?

Over the past 75 years, we have observed that investments with the highest average annual returns also tend to have the highest standard deviations of their annual returns. This observation supports the notion that there is a positive correlation between risk and return. Which of the following lists correctly ranks investments ...continues

SciLab : Resistance in a Network Circuit

Please see the attached file for the fully formatted problems.

Asymptotes and Ratio Limit Theorem

Show that if 1 < a < b, then a^n = O(b^n).

SciLab

Please see the attached file for the fully formatted problems. Problem 1 Consider the following two functions C x =∫0 x cost2 dt S  x =∫0 x sin t2 dt Write a program called 1.sce generates plots of these functions over the range 0≤x&# ...continues

Probability

A manufacturer of window frames know from long experience that 5 percent of the production will have some type of minor defect tht will require an adjustment. What is the probability that in a sample of 20 window frames a) none will need adjustment b) at least one will need adjustment c) More than two will need adjustment

Probabilities

Textbook authors and publishers work very hard to minimize the number of errors in text. However, some errors are unavoidable. The number of mean errors per chapter is 0.8. What is the probability that there are less than 2.