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Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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17. r(t) = (1²-21, 1+ 31, 31³ +21²), t = 18. r(t) = (tan ¹1, 2e²¹, 8te'), t = 0 19. r(t) = cos ti + 3tj + 2 sin 2rk, 20. r(t) = sin²ti + cos²t j + tan² tk, t = π/4 t = 0 21. If r(t) = (t, t², t³), find r'(t), T(1), r"(t), and r'(t) × r"(t). 22. If r(t) = (e², e-21, te 2¹), find T(0), r"(0), and r'(t) r"(t). 23-26 Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. et 2-1. 23. x = ² + 1, y = 4√t, z = e¹²¹; (2, 4, 1) 24. x = ln(t + 1), y = t cos 2t, z = 2¹; (0, 0, 1) 25. x = e cos t, (1, 0, 1) (2, ln 4, 1) M 26. x = √√√² + 3, -t y = e' sin t, z = e¹; y = ln(t² + 3), z = t; 16th 2 27. Find a vector equation for the tangent line to the curve of intersection of the cylinders x² + y² = 25 and y² + z² = 20 at the point (3, 4, 2). 28. Find the point on the curve r(t) = (2 cos t, 2 sin t, e), 0≤t≤T, where the tangent line is parallel to the plane √√3x + y = 1. 29-31 Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. Illus- trate by graphing both the curve and the tangent line on a common
Transcribed Image Text:17. r(t) = (1²-21, 1+ 31, 31³ +21²), t = 18. r(t) = (tan ¹1, 2e²¹, 8te'), t = 0 19. r(t) = cos ti + 3tj + 2 sin 2rk, 20. r(t) = sin²ti + cos²t j + tan² tk, t = π/4 t = 0 21. If r(t) = (t, t², t³), find r'(t), T(1), r"(t), and r'(t) × r"(t). 22. If r(t) = (e², e-21, te 2¹), find T(0), r"(0), and r'(t) r"(t). 23-26 Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. et 2-1. 23. x = ² + 1, y = 4√t, z = e¹²¹; (2, 4, 1) 24. x = ln(t + 1), y = t cos 2t, z = 2¹; (0, 0, 1) 25. x = e cos t, (1, 0, 1) (2, ln 4, 1) M 26. x = √√√² + 3, -t y = e' sin t, z = e¹; y = ln(t² + 3), z = t; 16th 2 27. Find a vector equation for the tangent line to the curve of intersection of the cylinders x² + y² = 25 and y² + z² = 20 at the point (3, 4, 2). 28. Find the point on the curve r(t) = (2 cos t, 2 sin t, e), 0≤t≤T, where the tangent line is parallel to the plane √√3x + y = 1. 29-31 Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. Illus- trate by graphing both the curve and the tangent line on a common
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