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t, 0st<1 3. f(t) = t21

t, 0st<1 3. f(t) = t21

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Do problems 3, 5, 8, 10, 14, 17, 25, 29, 31, 37, 40.
In Problems 1–18 use Definition to find L{f(t)}. 10. f(f)- -1, 0<t<1 C+ 1. f(t) = 1, t21 a [4, 0st<2 2. f(t) = [0, t2 2 FIGURE 7.1.9 Graph for Problem 10 t, 0st<1 3. f(t) = 1, 11. f(t) = e'+7 12. f(t) = e-21-5 t2 1 13. f(t) = te4' 14. f(t) = t²e¬2t 2t + 1, 0<t<1 [0, ( sin t, 0<t < 4. f(t) = 15. f(t) = e-' sin t 16. f(t) = e' cos t t21 17. f(t) = t cos t 18. f(t) = t sin t 5. f(t) = [0, In Problems 19–36 find L{f(t)}. 0, 6. f(t) = 0 <t< T/2 |cos t, tz T/2 19. f(t) = 2tª 20. f(t) = t5 21. f(t) = 4t – 10 22. f(t) = 7t + 3 7. f(t) 4 (2, 2) 23. f(t) = t² + 6t – 3 24. f(t) = -4t² + 16t + 9 1+ 25. f(t) = (t + 1)³ 26. f(t) = (2t – 1) 27. f(t) = 1 + e4t 28. f() 3 12 — е 9 + 5 1 FIGURE 7.1.6 Graph for Problem 7 29. fO) 3 (1 + е?)? 30. f(t) = (e' – e¯)² f(1) + 31. f(t) = 4t² – 5 sin 3t 32. f(t) = cos 5t + sin 2t 8. (2, 2) 33. f(t) = sinh kt 34. f(t) = cosh kt 1+ 35. f(t) = e' sinh t 36. f(t) = e¯ cosh t 1 In Problems 37–40 find L{f(t)} by first using a trigono- metric identity. FIGURE 7.1.7 Graph for Problem 8 9. f(t) 4 37. f(t) = sin 2t cos 2t 38. f(t) = cos²t 39. f(t) = sin(4t + 5) 40. f(t) = 10 cos t FIGURE 7.1.8 Graph for Problem 9
Transcribed Image Text:In Problems 1–18 use Definition to find L{f(t)}. 10. f(f)- -1, 0<t<1 C+ 1. f(t) = 1, t21 a [4, 0st<2 2. f(t) = [0, t2 2 FIGURE 7.1.9 Graph for Problem 10 t, 0st<1 3. f(t) = 1, 11. f(t) = e'+7 12. f(t) = e-21-5 t2 1 13. f(t) = te4' 14. f(t) = t²e¬2t 2t + 1, 0<t<1 [0, ( sin t, 0<t < 4. f(t) = 15. f(t) = e-' sin t 16. f(t) = e' cos t t21 17. f(t) = t cos t 18. f(t) = t sin t 5. f(t) = [0, In Problems 19–36 find L{f(t)}. 0, 6. f(t) = 0 <t< T/2 |cos t, tz T/2 19. f(t) = 2tª 20. f(t) = t5 21. f(t) = 4t – 10 22. f(t) = 7t + 3 7. f(t) 4 (2, 2) 23. f(t) = t² + 6t – 3 24. f(t) = -4t² + 16t + 9 1+ 25. f(t) = (t + 1)³ 26. f(t) = (2t – 1) 27. f(t) = 1 + e4t 28. f() 3 12 — е 9 + 5 1 FIGURE 7.1.6 Graph for Problem 7 29. fO) 3 (1 + е?)? 30. f(t) = (e' – e¯)² f(1) + 31. f(t) = 4t² – 5 sin 3t 32. f(t) = cos 5t + sin 2t 8. (2, 2) 33. f(t) = sinh kt 34. f(t) = cosh kt 1+ 35. f(t) = e' sinh t 36. f(t) = e¯ cosh t 1 In Problems 37–40 find L{f(t)} by first using a trigono- metric identity. FIGURE 7.1.7 Graph for Problem 8 9. f(t) 4 37. f(t) = sin 2t cos 2t 38. f(t) = cos²t 39. f(t) = sin(4t + 5) 40. f(t) = 10 cos t FIGURE 7.1.8 Graph for Problem 9
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