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19. r(t) = cos ti+ 3tj + 2 sin 2t k, t = 0

19. r(t) = cos ti+ 3tj + 2 sin 2t k, t = 0

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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14. r(t) 15. r(t) = a + b + t²c 16. r(t) = tax (b + c) 17-20 Find the unit tangent vector T(t) at the point with the given value of the parameter t. 17. r(t) = (t² − 2t, 1 + 3t, 1³ + 1/1²), t = 2 - 18. r(t) = (tan-¹t, 2e²¹, 8te'), t = 0 19. r(t) = cos ti + 3tj + 2 sin 2tk, t = 0 20. r(t) = sin²ti + cos²t j + tan² tk, t = π/4 A SUDA 21. If r(t) = (t, t², t³), find r'(t), T(1), r"(t), and r'(t) × r"(t). 22. If r(t) = (e²¹, 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. 23. x = 1² + 1, y = 4√t, z = e z = e¹² -¹; (2, 4, 1) z = 2¹; (0,0,1) 24. x = ln(t + 1), y = t cos 2t, 25. x = e¹¹ cost, y=e¹ sint, z = e¹¹; (1,0,1) 26. x = √² + 3, y = ln(t² + 3), z = t; (2, In 4, 1) 27. Find a vector equation for the tangent line to the curve of intersection of the cylinders x² + y² = 25 and y² + ² = 20 at the point (3, 4, 2). e'),
Transcribed Image Text:14. r(t) 15. r(t) = a + b + t²c 16. r(t) = tax (b + c) 17-20 Find the unit tangent vector T(t) at the point with the given value of the parameter t. 17. r(t) = (t² − 2t, 1 + 3t, 1³ + 1/1²), t = 2 - 18. r(t) = (tan-¹t, 2e²¹, 8te'), t = 0 19. r(t) = cos ti + 3tj + 2 sin 2tk, t = 0 20. r(t) = sin²ti + cos²t j + tan² tk, t = π/4 A SUDA 21. If r(t) = (t, t², t³), find r'(t), T(1), r"(t), and r'(t) × r"(t). 22. If r(t) = (e²¹, 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. 23. x = 1² + 1, y = 4√t, z = e z = e¹² -¹; (2, 4, 1) z = 2¹; (0,0,1) 24. x = ln(t + 1), y = t cos 2t, 25. x = e¹¹ cost, y=e¹ sint, z = e¹¹; (1,0,1) 26. x = √² + 3, y = ln(t² + 3), z = t; (2, In 4, 1) 27. Find a vector equation for the tangent line to the curve of intersection of the cylinders x² + y² = 25 and y² + ² = 20 at the point (3, 4, 2). e'),
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