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37. 6² ( So 1 1 t + 1 i+ 1 t² + 1 j+ t t² + 1 2 k dt

37. 6² ( So 1 1 t + 1 i+ 1 t² + 1 j+ t t² + 1 2 k dt

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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At what point do the curves r(t) = (t, 1-t, 3+12) and intersection correct to the nearest degree. r₂(s) = (3-s, s2, s²) intersect? Find their angle of 40 Evaluate the integral. AT- 35. ² (ti − t³j + 3t³ k) dt 36. 37. J 38. 4 40. (21³/² i + (t + 1) √t k) dt 1 £ ( ₁ 1 FA 1 t -i+ + 1 q² īj = +₁³ + ² + 1 k) d dt TT/4 (sec t tan ti + t cos 2t j + sin² 2t cos 2tk) dt 39. § (sec²t i + t(t² + 1)³ j + t² ln t k) dt 1 —_-77 k) d² dt t te i j √ ( 1 ²³ 1 + — —_-₁³ + √/\ 1 t /1 t² 41. Find r(t) if r'(t) = 2ti + 3t²j + √rk and r(1) = i + j. 42. Find r(t) if r'(t) = ti + e'j + te'k and r(0) =i+j+k. 43. Prove Formula 1 of Theorem 3. 44. Prove Formula 3 of Theorem 3. 45. Prove Formula 5 of Theorem 3. 3. t), use 48. 49 50 5 5 5 5
Transcribed Image Text:At what point do the curves r(t) = (t, 1-t, 3+12) and intersection correct to the nearest degree. r₂(s) = (3-s, s2, s²) intersect? Find their angle of 40 Evaluate the integral. AT- 35. ² (ti − t³j + 3t³ k) dt 36. 37. J 38. 4 40. (21³/² i + (t + 1) √t k) dt 1 £ ( ₁ 1 FA 1 t -i+ + 1 q² īj = +₁³ + ² + 1 k) d dt TT/4 (sec t tan ti + t cos 2t j + sin² 2t cos 2tk) dt 39. § (sec²t i + t(t² + 1)³ j + t² ln t k) dt 1 —_-77 k) d² dt t te i j √ ( 1 ²³ 1 + — —_-₁³ + √/\ 1 t /1 t² 41. Find r(t) if r'(t) = 2ti + 3t²j + √rk and r(1) = i + j. 42. Find r(t) if r'(t) = ti + e'j + te'k and r(0) =i+j+k. 43. Prove Formula 1 of Theorem 3. 44. Prove Formula 3 of Theorem 3. 45. Prove Formula 5 of Theorem 3. 3. t), use 48. 49 50 5 5 5 5
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