Infinite series
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The document discusses infinite series and the divergence test. It notes that if the limit of the terms does not equal 0 as n approaches infinity, then the series must diverge. For example, the harmonic series of 1/n diverges even though the limit of the terms is 0. The document then discusses power series and lists learning objectives about finding the general term, writing infinite geometric series in sigma notation, and determining if they converge or diverge based on the common ratio.
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This document contains a 12 problem calculus assignment covering areas and volumes, with some problems designated as requiring a calculator and others as non-calculator. The problems progress from 1 to 12 and cover foundational calculus concepts like area and volume calculations.
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This document appears to be a practice test for an AP Calculus exam containing problems on area and volume. It has 3 problems to solve, with the first problem not allowing the use of a calculator and the second and third problems allowing calculator use. The problems are assessing skills in calculating area and volume.
Statistical measures categorical data presentation
1. The document contains survey results from 20 students regarding their hair and eye color. 50% of respondents had brown or black hair, and 50% had brown eyes.
2. The data is analyzed to observe relationships between hair and eye color. 25% of students with red hair had green eyes, while 20% of students with blue eyes had brown hair.
3. Cross tabulations show that hair color distribution varied for each eye color, and eye color distribution varied for each hair color, providing evidence that hair and eye color are dependent traits.
Statistical measures categorical data
This document discusses statistical measures for working with categorical data. It provides an example dataset on Titanic passengers with variables like class, gender, and survival status. It then shows how to organize this data into frequency tables, contingency tables, bar charts, and segmented bar charts. These visualizations allow examining relationships between the categorical variables like the dependence between passenger class and survival status. The document also discusses concepts like conditional and marginal distributions, independence, and dependence.
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Statistical measures categorical data presentation
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Infinite series
- 1. AP Calculus BC Infinite Series
- 4. Divergence Test The fact that lim𝑘->∞𝑎𝑘=0 does not guarantee that an infinite series converges. However, if lim𝑘->∞𝑎𝑘≠0, the series must diverge! For example, lim𝑘->∞1𝑘=0, but lim𝑘->∞𝑛=1𝑘1𝑛 diverges.
- 6. Power Series
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