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Infer that the nth root of a natural number is either a natural number or it is irrational.
Find an article through newspapers, magazines, professional journals, etc and find at least two examples of data that are best modeled using linear formulae.
Show that the sum from 0 to infinity of (1-x)x^n does not converge uniformly on [0,1]. What subintervals of [0,1] does it converge uniforlmly on?
Given a function f and a subset A of its domain, let f(A) represent the range of f over the set A; f(A)={f(x) : x belong to A}.
Show that if sum x_n converges absolutely and the sequence(y_n) is bounded then the sum x_n y_n converges.
Assume that A And B are nonempty, bounded above and satisfy B subset or equal of A. Show that sup B<= sup A
If A1,A2,A3,...,Am are each countable sets, then the union A1 U A2 U A3...U Am is countable.
Assume (a_n) is a bounded sequence with the property that every convergent subsequence of (a_n) converges to the same limit a belong to R.
Assume a_n and b_n are Cauchy sequences.Use a triangle inequality argument to prove c_n=Absolute value of a_n-b_n is Cauchy.
Show that if sum a_n converges absolutely then sum a^2_n also converges absolutely.Does this proposition hold without absolute converge.
A set F subset or equal to R is closed if and only if every Cauchy sequence contained in F has a limit that is also an element of F.
Provide a narrative that explains the Management Scientist solution used.
Rock from quarry #9 is not suitable for rock needed in quarry.Minimize travel needed accomplish all the rock removals and replacements
A company that makes bikes wants to maximize profit over the next five months.
Graphical Minimization.The ABC small-scale industry has production facilities for two different products.
Let x belong to O, where O is an open set.If (x_n) is a sequence converging to x prove that all but a finite number of the terms of (x_n) must be contained in O
Maximize the return on the investment.Referring to the information listed above, suppose the investor has changed his attitude about the investment
Formulate and solve a transportation problem."Transportation Problems" are a subclass of network flow problems.
Determining Waiting Times.McBurger's fast-food restaurant has a drive-through window with a single window
Let A and B be subsets of R show that if there exists disjoint open sets U and V with A subset or equal of U and B subset or equal of V then A and B.
Is there an example of a linear fractional transformation that maps the unit disk to the upper half plane and takes the unit circle to the real axis?
A set E is totally disconnected if, given any two points x,y belong to E there exist separated sets A and B with x belong to A and y belong to B and E=A U B.
Find the cost minimizing routing of generators from the four plants to the nine warehouses
A set B subset or equal to R is called G_&(G sigma) if it can be written asthe countable intersection of open sets.
If {G1,G2,G3,...} is a countable collection of dense, open sets then the intersection (U top infinity bottom n=1)G_n is not empty.