If A is a non-empty subset of R, show that the set B = {a∈Ā : ∃ε>0 such that (a, a+ε) ∩ A =∅} is at most countable. (where Ā denotes the closure of A). This is for...

If A is a non-empty subset of R, show that the set B = {a∈Ā : ∃ε>0 such that (a, a+ε) ∩ A =∅} is at most countable. (where Ā denotes the closure of A). This is for...

Show that the set GL(n, R) of invertible n × n real matrices is open in the space of n × n matrices, with the metric being the Euclidean metric in Rn^2 when a matrix is identiﬁed with a long, n2...

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Denoting, as usual, by (a, b) an ”open interval”, {x : a<x< b} and by [a, b] the corresponding ”closed interval”, {x : a≤x≤b} of real numbers, prove that sup(a, b)=sup[a, b]=b and inf(a, b)=inf[a,...

Since the infinite sum of the inverse squares is (pi^2 / 6), is the infinite sum of the squares equal to the inverse of (pi^2 / 6)?

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Consider points P = (0, a), Q = (c, b) in the plane, with a, b, c all positive. Find a point R = (x, 0) so that the distance P R+QR is minimal. Justify that your answer is indeed a minimum.

Describe how it could happen that three different animals could each be claimed -rightfully- to be the largest of the three. Discuss the implications of this kind of situation for teaching students...

TV Circuit has 30 large-screen televisions in a warehouse in Erie and 60 large-screen televisions in a warehouse in Pittsburgh. Thirty-five are needed in a store in Blairsville, and 40 are needed...

Write the polynomial equation if it has x - intercepts (-6,0) and (1,0) with a tangent at (1,0) and goes through the point (4,-30)

A construction company has dump trucks that hold 10 cubic yards. If the company's workers dig a hole that os 8 feet deep, 20 feet wide, and 30 feet long, then how many dump truck loads will they need...

Three marbles are drawn randomly WITH REPLACEMENT from a box with 5 blue and 7 green marbles. (a) What is the probability that all the marbles drawn are green? (b) What is the probability...

I'm having a lot of trouble trying to solve the equations algebraically on the interval (0,2pi). Any help is greatly appreciated! 1) tanx= 0 2) 4sin^2x-1=0

Find the definite integral of the function cosx at points from a to b by definition.

ACME company's expected sales can be modeled by g(t)=t^3-2t^2+4t-7, where g(t) is measured in thousands of dollars and t is the number of years after 2008.

I'm having trouble finding the missing sides and angles for the triangle. I know you have to use law of sines to find them, but I'm having trouble. Any help is greatly appreciated! A=...

Q1 prove piecewise convergent on (0,infinity) Q2 prove uniform convergent on [1,infinity) Please help with these two equations. Much Thanks, it's preparation for final exam...

Q1 prove piecewise convergent on (0,infinity) Q2 prove uniform convergent on [1,infinity) Please help with these two equations. Much Thanks, it's preparation for final exam...