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Let f, g : R → R be continuous functions. (a) Prove that if f(r) = 0 for all r ∈ Q, then f(x) = 0 for all x ∈ R. (b) Prove that if f(r) = g(r) for all r ∈ Q, then f(x) = g(x) for all x ∈ R.
How should I go about this problem using sequences? For example, can I form a sequence r-sub-n ----> x and somehow use that show f(x) = 0?
Encoding single letters one by one is rather limiting, since there are only 26 possible messages. - What is the general procedure for finding the number corresponding to a digraph?
Determining the dimensions of a rectangle of maximum area that is formed by x- axis and a semi circle - What length and width should the rectangle have so that its area is a maximum?
A very important skill to have is the ability to read a sentence and translate it into a mathematical expression, equation, or inequality. Below I have three sentences that I would like you to translate into inequalities. Once complete, write three..
Describe a political poll or survey. Analyze the number of people who participated in the sample compared to the number in the population. Discuss how the results of the survey can be used to tell a story or support an idea of the sponsoring compan..
A correlation has been calculated as r = -0.8, what does this mean? How does it compare to a correlation of r = 0.8?
a farmer purchases 730 feet of fencing to enclose a rectangular garden. If the length of the garden is 5 feet more than 3 times the width. what is the dimensions of the garden?
Assuming that the results of a preliminary survey are not available. What is the most conservative estimate of the sample size that would limit the margin of error to within 0.05 of the population proportion for a 95% confidence interval?
At the instant shown in the sketch, the length of the kite string is 200 feet and the child is releasing string at the rate of 9 ft/sec. What is the rate of change for the angle of elevation from the child to the kite?
A spherical tank of radius 3m is half full of oil that has a density of 900kg/m3. Find the work W required to pump the oil out of a spout which extends 1.5m past the top of the sphere. (Use 9.8 for g and 3.14 for . Round your answer to three signi..
Suppose that you have been hired as an economic consultant by OPEC and given the following schedule showing the world demand and supply for oil.
What statistical analysis will test for this, plus one other variable on a skill the teachers were supposed to learn?
Two tracking stations are on the equator 119 miles apart. A weather balloon is located on a bearing of N 35°E from the western station and a bearing of N 22°E from the eastern station. How far, to the nearest mile, is the balloon from the western ..
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