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17. r(t) (te, 2 arctan 1, 2e¹), 1-0

17. r(t) (te, 2 arctan 1, 2e¹), 1-0

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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Question
Number 17
13. r(t) = e¹¹i − j + ln(1 + 3r) k 14. r(t) at cos 3ri + b sin³rj + c cos³t k 15. r(t) =a + rb + f²c 16. r(t)tax (b + c) 17-20 Find the unit tangent vector T() at the point with the given value of the parameter 1. 17. r(t) (te, 2 arctan 1, 2e'), 1–0 18. r(t) = (z³ + 31, 1² + 1,31 + 4), 1 – 1 19. r(7) = cos /i + 3j + 2 sin 2/ k, 20. r(1) = sin²zi + cos²zj + tan²1 k, 1 = π/4 P 21. If r(1) – (1, 1², 1³), find r'(7), T(1), r"(7), and r'(7) × r”(1). 22. If r(t) (e¹,e2, te"), find T(0), r”(0), and r¹(7) · r”(1). 23-26 Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. 23. x1 + 2√7. y − 1 − 1, 2− 1'³ +1: (3.0.2) 24. xe¹. y—_le',_- — te'. (1.0.0) 25. xecos 1. 1 sin /. 5-2 11, 0, 1) 26. 2-12 27. Find a vector equation for the tangent line to the curve of inter- section of the cylinders a 25 and y 20 at the point (3.4.2) 28. Find the point on the surve rızı 0277 where the tangent line is parallel to the plane
Transcribed Image Text:13. r(t) = e¹¹i − j + ln(1 + 3r) k 14. r(t) at cos 3ri + b sin³rj + c cos³t k 15. r(t) =a + rb + f²c 16. r(t)tax (b + c) 17-20 Find the unit tangent vector T() at the point with the given value of the parameter 1. 17. r(t) (te, 2 arctan 1, 2e'), 1–0 18. r(t) = (z³ + 31, 1² + 1,31 + 4), 1 – 1 19. r(7) = cos /i + 3j + 2 sin 2/ k, 20. r(1) = sin²zi + cos²zj + tan²1 k, 1 = π/4 P 21. If r(1) – (1, 1², 1³), find r'(7), T(1), r"(7), and r'(7) × r”(1). 22. If r(t) (e¹,e2, te"), find T(0), r”(0), and r¹(7) · r”(1). 23-26 Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. 23. x1 + 2√7. y − 1 − 1, 2− 1'³ +1: (3.0.2) 24. xe¹. y—_le',_- — te'. (1.0.0) 25. xecos 1. 1 sin /. 5-2 11, 0, 1) 26. 2-12 27. Find a vector equation for the tangent line to the curve of inter- section of the cylinders a 25 and y 20 at the point (3.4.2) 28. Find the point on the surve rızı 0277 where the tangent line is parallel to the plane
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