Download e-book for iPad: Calculus I (SparkCharts) by SparkNotes Editors

By SparkNotes Editors

ISBN-10: 1586636235

ISBN-13: 9781586636234

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SparkChartsTM—created by means of Harvard scholars for college students everywhere—serve as learn partners and reference instruments that hide quite a lot of university and graduate college topics, together with enterprise, desktop Programming, drugs, legislations, international Language, Humanities, and technology. Titles like how one can learn, Microsoft observe for home windows, Microsoft Powerpoint for home windows, and HTML provide you with what it takes to discover good fortune at school and past. Outlines and summaries hide key issues, whereas diagrams and tables make tough suggestions more straightforward to digest.

This four-page chart comprises reviews:
Definition of calculus and functions
Types of capabilities and rules
Trigonometric identities
Limits and continuity
Taking derivatives
Using derivatives

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Extra resources for Calculus I (SparkCharts)

Example text

The proof in Chou Pei Suan Ching is based on this diagram from the text. In this exercise we explain the details of the proof. C 34. This problem indicates a method for calculating the area of a triangle when the coordinates of the three vertices are given. (a) Calculate the area of ^ABC in the figure. y C(7, 8) B(8, 5) A(3, 4) x A diagram accompanying a proof of the “Pythagorean” theorem in the ancient Chinese text Chou Pei Suan Ching [from Science and Civilisation in China, vol. 3, by Joseph Needham (Cambridge, England: Cambridge University Press, 1959)].

Were you correct about which estimate was the most reliable and which was the least? If you missed either one, how might you adjust the reasons or intuitions that you expressed in part (a)? 0 P ( percentage) 1955 F (Fahrenheit temperature) t (year) Figure A Figure B Figure C Global average temperature at Earth’s surface Some correspondences between temperatures on the Celsius and Fahrenheit scales. 5 GRAPHS AND GRAPHING UTILITIES In this section we look at the connection between two basic skills that you’ve worked on in previous courses: • • graphing equations solving equations We also look at these topics in terms of graphing utilities.

X ϩ 2)(x ϩ 1) ϭ x 2 ϩ 11 11. t Ϫ {4 Ϫ [t Ϫ (4 ϩ t)]} ϭ 6 y x 2x Ϫ11 ϭ 12. ϩ 13. 1 Ϫ ϭ 6 3 5 5 3 1 xϪ1 2x ϩ 3 4 ϩ ϭ0 14. 15. ϭ Ϫ 1 4 Ϫ1 x x 1 1 3 1 2 1 Ϫ ϭ 2 16. ϩ 1 ϭ Ϫ 17. y y 2y xϪ3 xϩ3 x Ϫ9 1 2x ϩ 1 1 ϩ ϭ 2 18. xϪ5 xϩ5 x Ϫ 25 1 4 4 ϩ ϭ 2 xϩ2 xϪ2 x Ϫ4 4 2 3 20. Ϫ ϭ 2 2x ϩ 1 xϩ1 2x ϩ 3x ϩ 1 5 1 3 21. ϭ Ϫ 2 xϪ4 2x ϩ 3 2x Ϫ 5x Ϫ 12 2 3 5 3 22. (a) 23. (a) ϭ ϭ 3x x xϪ2 9x 3 2 3 5 (b) (b) ϭ ϭ 3x xϩ1 xϪ2 9x Ϫ 2 3 5 3 2 ϭ ϩ1 ϭ5 (c) (c) 3x x xϪ2 3x Ϫ 2 19. In Exercises 24 – 33, solve each equation by factoring.

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Calculus I (SparkCharts) by SparkNotes Editors


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