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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TIME SERIES ANALYSIS Introduction Economic and business time series analysis is a major field of research and application. This analysis method has been used for economic forecasting‚ sales forecasting‚ stock market analysis and company internal control. In this paper‚ we will talk about time series and review techniques that are useful for analyzing time series data. Definition of Time Series and Time Series Analysis Time series is an ordered sequence of values of a variable at equally spaced
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Title of Experiment: An Activity Series Lab MSDS: Copper‚ Cu(s) Stability- Stable. Incompatible with strong acids‚ active halogen compounds‚ chlorine‚ fluorine‚ iodine‚ bromine‚ ammonia. May react explosively with strong oxidizing agents. Toxicology-Dust may cause respiratory irritation. Personal Protection- Suitable ventilation if handling powder. Zinc‚ Zn(s) Stability-Stable. Incompatible with amines‚ cadmium‚ sulfur‚ chlorinated solvents‚ strong acids‚ strong bases. Air and moisture
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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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BMW: THE 7-SERIES PROJECT mary lou Brief History of Bayerische Motoren Werke: BMW‚ a German company is a producer of automobiles and motorcycles. Designed as an aircraft manufacturer and originally founded in 1913 by Karl Fredrich Rapp‚ the company was commissioned to build the V-12 engine for Austria-Hungary. In need of extra financing‚ Rapp reconstructed the company as the Bayerische Motoren Werke. In 1917‚ Rapp left the company and it was taken over by Austrian Franz Josef Popp who
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through networks. The resultant output signal is dependent on the properties of both the input signal and the processes acting on the signal. This is a laboratory Report will be focusing on using Fourier series to analyze waveforms and the synthesis of waveforms. The report highlights Fourier series analysis is a simple effective approach to analyse periodic signals. It will guide the reader through an experiment conducted in a lab to examine the effects of using Fourier analysis on signals and their
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December 2008 SDL SERIES‚ ARTICLE #4 SDL Series - Article #4: Threat Modeling at Microsoft In this fourth article in the series‚ we examine how Microsoft uses a technique known as “threat modeling” to detect design issues that could result in product vulnerabilities. Threat modeling is one component of the Microsoft Security Development Lifecycle (SDL). Content The Microsoft SDL What is Threat Modeling? A Security Frame of Mind The Threat Modeling Process Mitigating Threats Threat Modeling
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In 2003‚ Rob Zombie wrote and directed House of 1000 Corpses‚ a film about four young adults who end up off the beaten path and in the house of an evil‚ murderous family. The film takes place in a small‚ run down rural town during the 1970s. In the director’s commentary‚ Zombie describes his motion picture as a “70s exploitation horror film.”(House of 1000 Corpses.) He also mentions that he was inspired by the alleged Manson family home videos. He makes subtle parallels between the Firefly family
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Accountability is defined by department of defense as the obligation imposed by a law or lawful order or regulation on an officer or other person for keeping an accurate record of government property‚ documents or funds. The numerical end product of personnel accountability process reflects the combat power of a unit. So what is Personnel accountability exactly? Personnel accountability is a by name tracking system that manages the duty status and location of every single soldier assigned or
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Philosophy Exam 1 Notes Contd. • The Value of Philosophy – Bertrand Russell o Studying Philosophy Alleviates Prejudice ▪ Philosophy is of value. Most men‚ at the hands of science‚ believe that philosophy is useless ▪ The fault is in the way philosophy appears to people. Many people have a wrong conception of what philosophy is and wants to achieve. Just as physical science is helpful to many ignorant people‚ philosophy is helpful indirectly on lives
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