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1. Let f:R->R be uniformly continuous on R (the reals) and let f_n(x)=f(x+1/n) for x in the reals. Show that (f_n) converges uniformly on the reals to f.
2. Suppose that the sequence (f_n) converges uniformly to f on the set A, and suppose that each f_n is bounded on A. (That is, for each n there is a constant M_n such that |f_n(x)| < M_n for all x in A). Show that the function f is bounded on A.
3. Let f_n(x) = nx/(1+nx^2) for x in A =[0,infinity). Show that each f_n is bounded on A, but the point-wise limit f of the sequence is not bounded on A. Does (f_n) converge uniformly to f on A? Hint: f_n(1/squareroot(n))=squareroot(n)/2, where squareroot n= n^0.5.
4. Let f_n(x) =(x^n)/n for x in [0,1]. Show that for the sequence (f_n) of differentiable functions converges uniformly to a differentiable function f on [0,1], and that the sequence (f'_n) converges on [0,1] to a function g, but that g(1) does not equal f'(1).
Calculating Production and Material Consumption Rates, The Ottawa Coat company manufactures winter coats and spring jackets. The winter coat requires 4m of material while the spring jacket requires just 1m
Application of differential calculus in economics: Profit, Cost and Revenue function - What is the maximum profit if each item is sold for $7? (Assume you sell every thing you produce.)
Graph the functions y=x and y= square root of x on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.
Develop a joint probability table. Develop a probability tree showing all marginal, conditional, and joint probabilities.
Also, if the variables in an equation were reversed, what would happen to the graph of the equation? This was the example I was given, how would the graph of y = x² relate to the graph of x = y²?
Explain all the different factors that might cause a confidence interval for μy/x0 to increase in width. [There are five. Look at the formula for the confidence interval, but please EXPLAIN THE FACTORS THAT COULD MAKE THE INTERVAL WIDER IN PLAIN ENGL..
An estimated 8% of men and O.5% of women are colorblind. If a colorblind person is selected at random, what is the probability that the person is a man?
Find the probability that a bag of fertilizer will weigh between 45 and 55 pounds?
Parke-Davis data: A group of 100 people were in a study involved treatment with Lipitor. Unbeknownst to the subjects, some of them were given Liptor and some were given placebo (sugar pill) as shown in the table.
How do you solve for the conditional probability of a false positive for a cancer test?, An experimental test to detect a particular type of cancer indicates the presence of cancer in 90% of individuals known to have this type of cancer, and in 15..
Estimate the expected grade & variance for the course
A fire detection sensor is tested for its failure rate and found to have a mean failure rate of 3.6E-2 per hour of exposure with a standard deviation of
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