I have to find if they are removable or unremovable.Solution .pdf

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I have to find if they are removable or unremovable. Solution denominator can be written as =x^2 + 3x - 10 = (x+5)(x-2) therefore the function is discontinuous at 2 and -5 the discontinuity at 2 is removable because f(x) = (x-2)/((x-2)(x-5)) = 1/(x-5).

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I managed to do this in terms of polar coordinates. How would one solve this using the fact that T(z) = z^2? (2) Consider the map T: D D, where D is the unit disk in the plane, given by T(r cos theta, r sin theta) = (r^2 cos 2theta,r2 sin 2theta), Using complex notation, z = x + iy, the map T can be written as T(z) = z^2, Show that the Jacobian determinant of T vanish only at the origin. Thus, away from the origin, T is locally one-to-one. However, show that T is not globally one-to- one on 2 minus the origin. Solution T(z) = T(rcost, rsint) Consider z^2 = (rcost, rsint).(rcost,rsint) = r^2cos^2t+r^2sin^2t = r^2 = (x^2+y^2) where x =rcost and y =rsint Thus T(z) = z^2 T(z) = z^2 =0 only when r=0 or at the origin. As T(z) = z^2, T(-z) = (-z)^2 =z^2 Thus z and -z have the same image under T. T is not one to one..

I managed to do this in terms of polar coordinates. How would one so.pdf

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I have been reading the work of Alesina , about the pros and cons of dollarization (i.e. adopting the currency of other country, say the dollar). It is not the case of the European Union by the way, here the small open economy completely gives up on having its own currency. Countries like Panama, El Salvador, and Ecuador have adopted such monetary policy and have done well during expansionary part of the cycle. Now, most commodities prices, of which these countries depends are down, and evidence will be available of the costs of dollarization. However, here I ask about theoretical reasons of why this extreme fixed exchange rate is better with a flexible scheme. The trade-off is between stable and credible monetary policies and flexible possibly manipulable ones in countries with weak institutions. Solution Like many questions in economics, optimal behavior depends on the set of alternatives. The alternatives of Panama, El Salvador, and Ecuador to dollarization are likely a heavily politicized monetary and exchange rate policy. And so for the hypothetical small open economy considered in the question, the key issue is \"What\'s the institutional effectiveness and independence of the potential monetary authority?\" There are small, open economies with well run central banks (Australia and Switzerland) but also less well run ones (Turkey). If Panama could have Australia\'s quality of central bank they\'d probably prefer that to dollarization. That might explain why Chile and Costa Rica, with some of the best institutions in Central America choose not to peg their currency to the dollar. If Panama did manage its own monetary affairs without a peg they\'d get likely get results more like Turkey. They likely prefer dollarization to the results they\'d expect from independent monetary policy. And indeed, when you peek into the past of many countries with pegged currencies, you often find an episode of poorly conducted monetary policy just before dollarization. Not Panama (never had its own currency since independence), nor El Salvador, but Ecuador introduced dollarization in response to a severe banking and financial crisis. Argentina also seemed to introduce dollarization in response to monetary crisis. There are of course other considerations related to optimal currency areas. In particular, if you do a lot of trade with the USA dollarization is less of a sacrifice with respect to the best possible independent currency and monetary policy then if you do most of your trade with a neighboring country that uses a different currency. If Mexico adopts a pegged currency at some point the dollar makes a lot more sense than the Euro when 70% of their trade is with the USA and trade is a big part of their economy. But neighboring countries often have similar trading partners, and are in a similar position with respect to other optimal currency area criteria (no labor mobility to the reference country, no fiscal transfer mechanism shared with the reference .

I have been reading the work of Alesina , about the pros and cons of.pdf

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I know that real numbers consist of the natural or counting numbers,.pdf

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I just need problem 3Find the the sum of the series12^4 + 14.pdf

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I have been assigned to take the data and arrange it in the order I collected it (11,12,12,9,8.5,9.5,8.5,11,10,9,16,12,10,12,14). Count the total number of observations you have, and label this number N. Then create another set of data starting from one and increasing by one until you reach N (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15). This set of data is called a time series. Runa regression using the original set of data as the dependent variable, and your time series as an independent variable. What are the results and any conclusions that can be reached by the results? Solution total number of observations(N):15 dependent variabl(x)=11,12,12,9,8.5,9.5,8.5,11,10,9,16,12,10,12,14 independent variable(y)=1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 The equation for a straight line is usually written as: Y = bX + a where b = slope of the line = (Y2 - Y1) / (X2 - X1) = “the rise” divided by “the run” and a = the Y-intercept = the value of Y when X = 0 Y=X+165.5.

I have been assigned to take the data and arrange it in the order I .pdf

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I hope someone can help me , I need to write a ten page paper on Probability by 215-2012. Is there any out there that can help me with this problem? Solution Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we are not certain.[1] The proposition of interest is usually of the form \"Will a specific event occur?\" The attitude of mind is of the form \"How certain are we that the event will occur?\" The certainty we adopt can be described in terms of a numerical measure and this number, between 0 and 1, we call probability.[2] The higher the probability of an event, the more certain we are that the event will occur. Thus, probability in an applied sense is a measure of the likeliness that a (random) event will occur. The concept has been given an axiomatic mathematical derivation in probability theory, which is used widely in such areas of study as mathematics, statistics, finance, gambling, science, artificial intelligence/machine learning and philosophy to, for example, draw inferences about the likeliness of events. Probability is used to describe the underlying mechanics and regularities of complex systems. The word probability does not have a singular direct definition for practical application. In fact, there are several broad categories of probability interpretations, whose adherents possess different (and sometimes conflicting) views about the fundamental nature of probability. For example: Frequentists talk about probabilities only when dealing with experiments that are random and well-defined. The probability of a random event denotes the relative frequency of occurrence of an experiment\'s outcome, when repeating the experiment. Frequentists consider probability to be the relative frequency \"in the long run\" of outcomes.[3] Subjectivists assign numbers per subjective probability, i.e., as a degree of belief.[4] Bayesians include expert knowledge as well as experimental data to produce probabilities. The expert knowledge is represented by a prior probability distribution. The data is incorporated in a likelihood function. The product of the prior and the likelihood, normalized, results in a posterior probability distribution that incorporates all the information known to date. The scientific study of probability is a modern development. Gambling shows that there has been an interest in quantifying the ideas of probability for millennia, but exact mathematical descriptions arose much later. There are reasons of course, for the slow development of the mathematics of probability. Whereas games of chance provided the impetus for the mathematical study of probability, fundamental issues are still obscured by the superstitions of gamblers.[8] According to Richard Jeffrey, \"Before the middle of the seventeenth century, the term \'probable\' (Latin probabilis) meant approvable, and was applied in that sense, univocally, to opinion and to action. A probable action or opinion was one such .

I hope someone can help me , I need to write a ten page paper on Pro.pdf

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I hope i did all of that correctly.Can someone check my math o.pdf

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