Multivariable Calculus: Early Transcendentals, 6th Edition by James Stewart

By James Stewart

Luck on your calculus path begins the following! James Stewart's CALCULUS texts are world-wide best-sellers for a cause: they're transparent, actual, and jam-packed with proper, real-world examples. With CALCULUS: EARLY TRANCENDENTALS, 6th version, Stewart conveys not just the application of calculus that will help you boost technical competence, but in addition offers an appreciation for the intrinsic great thing about the topic. His sufferer examples and integrated studying aids may also help you construct your mathematical self belief and attain your pursuits within the direction!

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Extra resources for Multivariable Calculus: Early Transcendentals, 6th Edition

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The corresponding point on C is (0, 0). (c) To determine concavity we calculate the second derivative: x 2 d y ෇ dx 2 t=1 (1, _2) 3 (x-3) y=_ œ„ FIGURE 1 y ෇ Ϫs3 ͑x Ϫ 3͒ and d dt ͩ ͪ ͩ ͪ dy dx dx dt ෇ 3 2 1ϩ 2t 1 t2 ෇ 3͑t 2 ϩ 1͒ 4t 3 Thus the curve is concave upward when t Ͼ 0 and concave downward when t Ͻ 0. (d) Using the information from parts (b) and (c), we sketch C in Figure 1. V EXAMPLE 2 (a) Find the tangent to the cycloid x ෇ r͑␪ Ϫ sin ␪ ͒, y ෇ r͑1 Ϫ cos ␪ ͒ at the point where ␪ ෇ ␲͞3.

In general, how is the graph of r ෇ f ͑␪ Ϫ ␣͒ related to the graph of r ෇ f ͑␪ ͒? ¨ O 84.

Y (b) Find parametric equations to represent the line segment from ͑Ϫ2, 7͒ to ͑3, Ϫ1͒. ; 32. Use a graphing device and the result of Exercise 31(a) to a draw the triangle with vertices A ͑1, 1͒, B ͑4, 2͒, and C ͑1, 5͒. b P ¨ 33. Find parametric equations for the path of a particle that x O moves along the circle x 2 ϩ ͑ y Ϫ 1͒2 ෇ 4 in the manner described. (a) Once around clockwise, starting at ͑2, 1͒ (b) Three times around counterclockwise, starting at ͑2, 1͒ (c) Halfway around counterclockwise, starting at ͑0, 3͒ 42.

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