Calculus - Early Transcendentals [intro txt] by S. Tan

By S. Tan

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Give the sign of the slope of each of the lines. b. List the lines in order of increasing slope. 6. Find the slope of each of the lines shown in the accompanying figure. 23. (Ϫ1, Ϫ2); L1 5 17. 13 1 13 20. 20 In Exercises 21–24, sketch the line through the given point with the indicated slope. 21. (1, 2); 3 y 1 2 15. Ϫ1 22. (2, 3); Ϫ1 Ϫ2 24. (Ϫ2, 3); 4 In Exercises 25–28, determine whether the lines through the given pairs of points are parallel or perpendicular to each other. 25. (1, Ϫ2), (Ϫ3, Ϫ10) and (1, 5), (Ϫ1, 1) L3 Ϫ4 0 Ϫ3 26.

These notations include e for the base of the natural logarithm, i for the square root of Ϫ1, and our commonly used function notation f(x). Euler made major contributions to every field of the mathematics of his time, and many of the concepts he developed bear his name today. Euler had a remarkable memory and was able to perform extremely complex calculations mentally. Johann Bernoulli (1667–1748) (page 624), his childhood tutor, recognized Euler’s exceptional mathematical ability and encouraged him to pursue a career in mathematics.

As an adult, Descartes spent some time in the army and eventually had a vision that convinced him of his divine mission to devise a new philosophical structure that would connect all branches of the sciences through mathematics and logic. During this period he began his most influential works: Le Geometrie and later the Meditations. The insights in Descartes’ work Le Geometrie laid the essential foundation for the work of Newton (page 202), Leibniz (page 179), and others in developing physics and calculus.

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