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13. r(t) = t sin ti + e' cos tj + sin t cos tk ht

13. r(t) = t sin ti + e' cos tj + sin t cos tk ht

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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(a) Sketch the plane curve with (b) Find r'(t). (c) Sketch the position vector r(t) and the tangent ve the given value of t.o 3. r(t) = (t - 2, t² + 1), t = -1 (9) 4. r(t) = (t², t³), t = 1 5. r(t) = e²¹ i + e'j, t = 0 30, 320 MASY 6. r(t) = e'i + 2tj, t = 0 7. r(t) = 4 sin ti - 2 costj, t = 3π/4 8. r(t) = (cost + 1) i + (sin t − 1)j, t= -π/3 9-16 Find the derivative of the vector function. 9. r(t) = (√t – 2, 3, 1/1²) 10. r(t) = (e¹, t - t³, In t) 11. r(t) = t² i + cos (t²)j + sin²t k 1 1+ t 12. r(t) = i+ t 1+ t 1 - k 1 + t J+1²+1²
Transcribed Image Text:(a) Sketch the plane curve with (b) Find r'(t). (c) Sketch the position vector r(t) and the tangent ve the given value of t.o 3. r(t) = (t - 2, t² + 1), t = -1 (9) 4. r(t) = (t², t³), t = 1 5. r(t) = e²¹ i + e'j, t = 0 30, 320 MASY 6. r(t) = e'i + 2tj, t = 0 7. r(t) = 4 sin ti - 2 costj, t = 3π/4 8. r(t) = (cost + 1) i + (sin t − 1)j, t= -π/3 9-16 Find the derivative of the vector function. 9. r(t) = (√t – 2, 3, 1/1²) 10. r(t) = (e¹, t - t³, In t) 11. r(t) = t² i + cos (t²)j + sin²t k 1 1+ t 12. r(t) = i+ t 1+ t 1 - k 1 + t J+1²+1²
(a) Sketch the plane curve with (b) Find r'(t). (c) Sketch the position vector r(t) and the tangent ve the given value of t.o 3. r(t) = (t - 2, t² + 1), t = -1 (9) 4. r(t) = (t², t³), t = 1 5. r(t) = e²¹ i + e'j, t = 0 30, 320 MASY 6. r(t) = e'i + 2tj, t = 0 7. r(t) = 4 sin ti - 2 costj, t = 3π/4 8. r(t) = (cost + 1) i + (sin t − 1)j, t= -π/3 9-16 Find the derivative of the vector function. 9. r(t) = (√t – 2, 3, 1/1²) 10. r(t) = (e¹, t - t³, In t) 11. r(t) = t² i + cos (t²)j + sin²t k 1 1+ t 12. r(t) = i+ t 1+ t 1 - k 1 + t J+1²+1²
Transcribed Image Text:(a) Sketch the plane curve with (b) Find r'(t). (c) Sketch the position vector r(t) and the tangent ve the given value of t.o 3. r(t) = (t - 2, t² + 1), t = -1 (9) 4. r(t) = (t², t³), t = 1 5. r(t) = e²¹ i + e'j, t = 0 30, 320 MASY 6. r(t) = e'i + 2tj, t = 0 7. r(t) = 4 sin ti - 2 costj, t = 3π/4 8. r(t) = (cost + 1) i + (sin t − 1)j, t= -π/3 9-16 Find the derivative of the vector function. 9. r(t) = (√t – 2, 3, 1/1²) 10. r(t) = (e¹, t - t³, In t) 11. r(t) = t² i + cos (t²)j + sin²t k 1 1+ t 12. r(t) = i+ t 1+ t 1 - k 1 + t J+1²+1²
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