Solution: Apply integral test: Z Z ln R 1 X R 2 1 p dx x (ln x) p=1 p 6= 1 let ln (x) = u then ln 2 so that when p = 1 and p < 1 integral diverges by letting R ! 1‚ so does the series. When p > 1 then integral converges to ! 1 p 1 p 1 p (ln R) (ln 2) (ln 2) lim = ‚ R!1 1 p 1 p 1 p so does the series. 2. (18 pts.) Find the in…nite sum 1 : n (n + 2) n=1 Solution: See that 1 1 = n (n + 2) n 1 n+2 1 X 8 R < ln ujln 2 ln 1 ln R du = 1 p : u p up 1 ln 2 hence 1 n (n + 2) n=1 k X
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Kiwi Series #1 My choice of artwork for this essay is titled Kiwi Series # 1. This painting is made by Dennis Wojtkiewicz in 2005. The size of this painting is 36 by 66 inches. The medium used in this painting is the oil on canvas. I chose this painting because it appeals to my sense of aesthetics and also it has the most interesting use of texture. This painting is an excellent example of our sight being able to activate other senses. The presentation of the translucent fruit and fuzzy skin is
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Experiment 19 - Determination of the equilibrium constant for the reaction Fe3+ (aq) + SCN( (aq) = FeSCN2+ (aq) Object: To determine the equilibrium constant by a colorimetric method Theory: Colorimetric methods of analysis are usually applied to the determination of small concentrations of either inorganic or organic materials in a solution. The constituent sought must be coloured or must be capable of reacting with a reagent to produce a substance having a suitable colour. Beers Law‚ which
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Learner’s Guide Manufacture craft baked flour confectionery products using the whisking method (No. 6) Unit Std # 6 NQF Level 3 Credit(s) 12 Field NSB 06: Manufacturing‚ Engineering and Technology Sub-Field Manufacturing and Assembly Issue date: July 2002 Review date: TBA Contents Why am I doing this? 3 At the end of the module you will 3 How to use this module 3 Introduction 4 5 Introduction baked flour confectionery products 6 11 The production of baked flour confectionery
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EFFICIENCY INCREASING SYSTEM BY USING PREHEATING METHOD EFFICIENCY INCREASING SYSTEM BY USING PREHEATING METHOD METHODOLOGY The concept of increasing the fuel efficiency of a petrol engine in this project‚ is to pre-heat the intake air which is flowing through the carburetor. The humidity in the atmospheric air affects the petrol vapourisation in the carburettor. Therefore‚ by pre-heating the inlet air to the carburettor for a considerable amount‚ the vapourisation can be ease and in turn
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Winter storm From Wikipedia‚ the free encyclopedia Jump to: navigation‚ search "Snowstorm" redirects here. For other uses‚ see Snowstorm (disambiguation). A winter storm is an event in which the dominant varieties of precipitation are forms that only occur at cold temperatures‚ such as snow or sleet‚ or a rainstorm where ground temperatures are cold enough to allow ice to form (i.e. freezing rain). In temperate continental climates‚ these storms are not necessarily restricted to the winter season
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[pic] Fourier Series: Basic Results [pic] Recall that the mathematical expression [pic] is called a Fourier series. Since this expression deals with convergence‚ we start by defining a similar expression when the sum is finite. Definition. A Fourier polynomial is an expression of the form [pic] which may rewritten as [pic] The constants a0‚ ai and bi‚ [pic]‚ are called the coefficients of Fn(x). The Fourier polynomials are [pic]-periodic functions. Using the trigonometric
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January February March April May June Demand 89 57 144 221 177 280 Month July August September October November December Demand 223 286 212 275 188 312 a. Determine the one-step-ahead forecasts for the demand for January 2000 using 3-‚ 6-‚ and 12-month moving averages. b. Using a four-month moving average‚ determine the one-step-ahead forecasts for July through December 1999. c. Compute MAD‚ MSE‚ MAPE for the forecasts obtained in b. Solution: a. MA (3) forecast: 258.33 MA (6) forecast: 249.33 MA (12)
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their customers in order to keep up with the times. Companies are required to display a creative outlook in their value offerings‚ advertising‚ packaging and delivering. Management of companies should show initiative and be willing to do new things and face new challenges in novel ways to get creative. Senior management in leading companies needs to determine the value of creativity then in their organization and see how it can be best managed. Holt (2002)‚ states that "Although creativity can
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SUMMER AND WINTER: TWO SEASONS WITH BIG DEFFERENCES When it comes to a question of the time of the year people prefer most‚ a majority answer based on two seasons‚ summer and winter. Summer and winter are two of the four seasons of the year‚ which have very vast differences and a few similarities. The first and most relevant difference is the change in weather‚ with summer having hot temperatures and winter with cold temperatures‚ which is seen from the metrological point of view. Using the temperature
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