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In Exercises 47-52, use Eq. (12) to find N at the point indicatee 47. (12,1), 1 = 1 %3D 48. (t- sin t, 1 – cos t), t=T

In Exercises 47-52, use Eq. (12) to find N at the point indicatee 47. (12,1), 1 = 1 %3D 48. (t- sin t, 1 – cos t), t=T

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 47

v(t)r"(1) – v'(t)r'(t) N(t) = 12 || v(1)r"(1) – v'(t)r'(t)|| %3D Hint: N is the unit vector in the direction T'(t). Differentiate T(t) = r'(t)/v(t) to show that v(t)r"(t) - v'(t)r'(t) is a positive multiple of T' (t). In Exercises 47-52, use Eg. (12) to find N at the point indicated. 47. (12,1), t = 1 48. (t- sin t, 1- cos t), t = T 49. (12/2,13/3, 1), 1 = 1 50. (t-1,t,12), t = -1 3D1 51. (t, e', t), t = 0 bor 52. (cosh t, sinht,t²), t= 0 53. Let r(t) = (1, $r³/2,1). %3D (a) Find T, N, and B at the point corresponding to t = = 1. (b) Find the equation of the osculating plane at the point corresponding t = 1.
Transcribed Image Text:v(t)r"(1) – v'(t)r'(t) N(t) = 12 || v(1)r"(1) – v'(t)r'(t)|| %3D Hint: N is the unit vector in the direction T'(t). Differentiate T(t) = r'(t)/v(t) to show that v(t)r"(t) - v'(t)r'(t) is a positive multiple of T' (t). In Exercises 47-52, use Eg. (12) to find N at the point indicated. 47. (12,1), t = 1 48. (t- sin t, 1- cos t), t = T 49. (12/2,13/3, 1), 1 = 1 50. (t-1,t,12), t = -1 3D1 51. (t, e', t), t = 0 bor 52. (cosh t, sinht,t²), t= 0 53. Let r(t) = (1, $r³/2,1). %3D (a) Find T, N, and B at the point corresponding to t = = 1. (b) Find the equation of the osculating plane at the point corresponding t = 1.
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