Limit at infinity The function has the limit as increases without bound (or‚ asapproaches infinity)‚ written if can be made arbitrarily close to by taking large enough. Similarly‚ the function has the limit as decreases without bound (or‚ asapproaches negative infinity)‚ written if can be made arbitrarily close to by taking to be negative and sufficiently large in absolute value. One-sided limits The function has the right-hand limit as approaches from the right written if the
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algorithm for the robust spanning tree problem with interval data R. Montemanni∗‚ L.M. Gambardella Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA) Galleria 2‚ CH-6928 Manno-Lugano‚ Switzerland Abstract The robust spanning tree problem is a variation‚ motivated by telecommunications applications‚ of the classic minimum spanning tree problem. In the robust spanning tree problem edge costs lie in an interval instead of having a fixed value. Interval numbers model uncertainty about the
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Chinese remainder theorem The Chinese remainder theorem is a result about congruences in number theory and its generalizations in abstract algebra. It was first published in the 3rd to 5th centuries by Chinese mathematician Sun Tzu. In its basic form‚ the Chinese remainder theorem will determine a number n that when divided by some given divisors leaves given remainders. For example‚ what is the lowest number n that when divided by 3 leaves a remainder of 2‚ when divided by 5 leaves a remainder
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Unit 1 Problem Set 1 26. Surgery Versus Splints A study compared surgery and splinting for subjects suffering from carpal tunnel syndrome. It was found that among 73 patients treated with surgery‚ there was a 92% success rate. Among 83 patients treated with splints‚ there was a 72% success rate. Calculations using those results showed that if there really is no difference in success rates between surgery and splints‚ then there is about 1 chance in 1000 of getting success rates like the ones obtained
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Chebyshev’s Theorem and The Empirical Rule Suppose we ask 1000 people what their age is. If this is a representative sample then there will be very few people of 1-2 years old just as there will not be many 95 year olds. Most will have an age somewhere in their 30’s or 40’s. A list of the number of people of a certain age may look like this: |Age |Number of people | |0 |1 | |1 |2 | |2 |3
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“The Arrow impossibility theorem and its implications for voting and elections” Arrow’s impossibility theorem represents a fascinating problem in the philosophy of economics‚ widely discussed for insinuating doubt on commonly accepted beliefs towards collective decision making procedures. This essay will introduce its fundamental assumptions‚ explain its meaning‚ explore some of the solutions available to escape its predictions and finally discuss its implications for political
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Econ 214 Problem Set 4 1. What determines whether a financial asset is included in the M1 money supply? Why are interest-earning checkable deposits included in M1‚ whereas interest-earning savings accounts and Treasury bills are not? A financial assest is included in the M1 money supply when it can be quickly converted into the physical form of money‚ such as dollars and coins. Interested-earning checkable deposits are included because it can be quickly accessible without limitations
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Baldeo Persaud NT 1230 Unit 5 Problem Set 1 Matching Complete the following exercise by matching the terms with their corresponding definitions. a. automated password guessing b. Windows authorization mechanism c. passwords plus smartcards d. stored in a digital certificate e. standard for smart card support f. decrypts data encrypted with a certificate g. firewall exceptions h. standard for fingerprint scanners and other devices i. potentially destructive software j. firewall rule requiring IPsec
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Problem Set – June 11th 1. How does our spatial representation of time constitute an element of consciousness? Jaynes outlines six essential features to consciousness in modern humans. The first is spatialization. This describes the ability to metaphorically construct abstract concepts in a spatial map. For example‚ think about human history from about 1000 AD to today. How did you conceive of this concept? Did you see a timeline running left to right‚ with bullet points for the Norman Conquest
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Problem Set 3 ECON 973 Fall 2012 Fluctuations: Discrete Time Models Ben Brewer 12/10/12 1. a. Given this two-period problem of labor supply maxc1 ‚n1 ‚c2 ‚n2 ln[c1 ] + ln[1 − n1 ] + βln[c2 ] + βln[1 − n2 ] subject to the intertemporal budget constraint c1 [1 + r] + c2 = w1 n1 [1 + r] + w2 n2 Dividing each side by [1+r] for convenience gives c1 + c2 w 2 n2 = w 1 n1 + 1+r 1+r We can solve for consumption and labor supply in each period (c1 ‚ c2 ‚ n1 ‚ n2 ) by first setting up the Lagrangian
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