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Math 104: Homework 7-
1. (a) Let S be a subset of R, and let f : S → R and g : R → R be uniformly continuous functions. Prove that the composition g ? f : S → R is uniformly continuous.
(b) Let f and g be two uniformly continuous functions from S to R. Prove that f + g is uniformly continuous.
(c) Show that there exist uniformly continuous functions f and g from S to R such that the multiplication f · g is not uniformly continuous.
2. Let f be a real-valued continuous function. Recall that for any subset S ⊆ R, then f(S) is defined as {f(x) : x ∈ S}. Suppose that f(I) is open for any open interval I. Prove that f is monotonic.
After solving parts A and B, assign the following parameter values and then use differential calculus to determine how long it will take for the oxygen concentration to reach the "sag" value.
Determine which candidate would have won if all of the preference ballots had been reversed. Does this election illustrate a violation of the reversal criterion?
explain why taking a series of markdowns is not the same as taking the total sum of the same markdowns. for example a markdown of 25% followed by a 30% is not the same as a 55% total markdown.
Bert borrowed $7500 from Delores on November 7, 1997. When Bert repaid the loan, Delores charged $190.02 interest. If the rate of simple interest on the loan was 6 3/4%, on what date did Bert repay the loan?
Find two (distinct) subgroups of order 30 in Z50 ⊕ Z60. Determine the number of elements of order 10 and the number of cyclic subgroups of order 10 in Z20 ⊕ Z15
Assume that a ball is expanding in the speed ot 60 cubic centimeters pet minute. What is the rate of its radius change when tlie ball has radius 10 centimeter.
explain in your own words the difference between zero divided by seven and seven divided by zero. show a way of writing
is there a significant difference in automobile insurance rates in different cities of comparable size in the u.s.? to
Need help solving a math question Solve the systems of equations by graphing. Check your solution.Y=-4x+23y+12x=6
A pendulum swings through an angle of 20 degrees each second.If the pendulum is 40 inches long, how fast is the tip of the pendulum swinging?
An equilateral triangle with sides of length 10 is inscribed in a circle. Find the distance from the center of the circle to any side of the triangle.
Trying to evaluate the double series in terms of p and q. below is the work
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