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25. / √ 11/12 19 14

25. / √ 11/12 19 14

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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25. √ 11/20 7 V 14 29. ex + 2 31. (-In 2, 35. y = K (
Transcribed Image Text:25. √ 11/20 7 V 14 29. ex + 2 31. (-In 2, 35. y = K (
ces. er fC ve e n n 17-20 (a) Find the unit tangent and unit normal vectors T(t) and N(t). (b) Use Formula 9 to find the curvature. 17. r(t) = (t, 3 cos t, 3 sin t) 18. r(t) = (t², sint - t cos t, cost + t sin t), t> 0 19. r(t) =(√2t, e'. e) 20. r(t) = (1, 1², 1²) TRAN 21-23 Use Theorem 10 to find the curvature. 21. r(t) = t³j+t² k 22. r(t) = ti + t²j+e'k 23. r(t) = √√√61² i + 2t j + 2t³ k 24. Find the curvature of r(t) = (t², In t, t In t) at the point (1, 0, 0). 25. Find the curvature of r(t) = (t, t², t³) at the point (1, 1, 1). 26. Graph the curve with parametric equations x = cos f, y = sin t, z = sin 5t and find the curvature at the point (1, 0, 0). 27-29 Use Formula 11 to find the curvature. 27. y = x² 28. y = tan x 30-31 At what point does the curve have maximum curvature? What happens to the curvature as x→∞o? 30. 29. y = xe* V = I
Transcribed Image Text:ces. er fC ve e n n 17-20 (a) Find the unit tangent and unit normal vectors T(t) and N(t). (b) Use Formula 9 to find the curvature. 17. r(t) = (t, 3 cos t, 3 sin t) 18. r(t) = (t², sint - t cos t, cost + t sin t), t> 0 19. r(t) =(√2t, e'. e) 20. r(t) = (1, 1², 1²) TRAN 21-23 Use Theorem 10 to find the curvature. 21. r(t) = t³j+t² k 22. r(t) = ti + t²j+e'k 23. r(t) = √√√61² i + 2t j + 2t³ k 24. Find the curvature of r(t) = (t², In t, t In t) at the point (1, 0, 0). 25. Find the curvature of r(t) = (t, t², t³) at the point (1, 1, 1). 26. Graph the curve with parametric equations x = cos f, y = sin t, z = sin 5t and find the curvature at the point (1, 0, 0). 27-29 Use Formula 11 to find the curvature. 27. y = x² 28. y = tan x 30-31 At what point does the curve have maximum curvature? What happens to the curvature as x→∞o? 30. 29. y = xe* V = I
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