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(1) Every convergent sequence contains either an increasing, or a decreasing subsequence.?
Proof: Suppose that lim(as n goes to infinity) x(sub n) = L. If infinitely many terms are equal to L, we are done. If not, either infinitely many terms are > L, or infinitely many terms are < L. Choose one option and complete the proof.(2) Adapt carefully the bisection argument seen in the proof of Bolzano-Weierstrass to prove the Intermediate Value
Theorem: If f is a continuous function on [a,b], and if f(a) and f(b) have opposite signs, then there exists a point c (a,b) such that f(c) = 0.
Proof: Suppose that f(a) < 0 and f(b) > 0. Denote a(sub 0) = a, b(sub 0) = b and consider the intervals [a, (a+b)/2] and [(a+b)/2, b].
This question is asking you to compare the likelihood of your getting 4 or more subscribers in a sample of 50 when the probability of a subscription has risen from 0.02 to 0.06.] Talk about the comparison of probabilities in your explanation.
Sketch a phase diagram corresponding to each of these cases. Try to make some general statements about the structure of equilibrium as a function of the parameters.
Find paremetric representations and sketch the path and what it the shape of the given contour - evaluate the function using Cauchy's integral formula and Find two sets of paremetric representations and sketch the path.
Your boss calls you into his office and he is extremely angry. He was embarrassed at a meeting because he put forward a recommendation that you had made and his idea was shot down by one of the technical geniuses in another department.
Calculate the upward force on the anchorage when the pipeline is flowing full. Calculate the upward force on the anchorage when the pipeline is empty. Assume density of steel is 7900kg/m3 and that of water is 1000kg/m3
Measure the quantities of the following items in the following drawing: Do not round the numbers in the middle of calculation. Write two decimal places to show the numbers used in your calculations procedures.
Analysis of the climograph, identifying the climate zone by name and Koppen-Geiger classification and a discussion of the controls on the climate that produce this pattern.
How much money will Dave and Jane raise for charity
Compare the results of i) to the exact solution and comment on the accuracy of the numerical algorithm and adopted step size.
Compute the amount of net income reported by Light for 20X2. In addition, prepare the stockholders' equity section of Light's balance sheet as of December 31, 20X2.
Where denotes the usual cross product of vectors. Sow that L is a Lie algebra and determine its structure constants relative to the standard basis for R3.
Use the Crank-Nicolson procedure to solve the following partial differential equation
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