SECTION 2.6 2.6 S Click here for solutions. 1–8 Evaluate the limit and justify each step by indicating the appropriate properties of limits. 1. lim 1 x sx 3. lim x⫹4 x 2 ⫺ 2x ⫹ 5 xl⬁ 共1 ⫺ x兲共2 ⫹ x兲 5. lim x l ⫺⬁ 共1 ⫹ 2x兲共2 ⫺ 3x兲 7. lim xl⬁ 1 3 ⫹ sx 2. lim xl⬁ 5 ⫹ 2x 3⫺x 7t ⫹ 4t 2t 3 ⫺ t 2 ⫹ 3 3 4. lim tl⬁ 6. 8. lim xl⬁ lim xl⬁ 冑 2x 2 ⫺ 1 x ⫹ 8x 2 sin 2x x2 rl⬁ r4 ⫺ r2 ⫹ 1 r5 ⫹ r3 ⫺ r s1 ⫹ 4x 2 11. lim xl⬁ 4⫹x 13. lim Stewart: Calculus: Early Transcendentals, Seventh Edtion. ISBN: 0538497904. © 2012 Cengage Learning. All rights reserved. xl⬁ 1 ⫺ sx 1 ⫹ sx 15. lim (sx 2 ⫹ 1 ⫺ sx 2 ⫺ 1 ) xl⬁ 16. lim (s1 ⫹ x ⫺ sx ) xl⬁ 3 3 17. lim (s 1⫹x⫺s x) 18. lim (sx 2 ⫹ x ⫹ 1 ⫹ x) 19. lim ( x ⫹ sx ) 20. lim 共x 3 ⫺ 5x 2 兲 xl⬁ t l⫺⬁ 6t 2 ⫹ 5t 共1 ⫺ t兲共2t ⫺ 3兲 sx 2 ⫹ 4x 12. lim x l⫺⬁ 4x ⫹ 1 14. lim (sx 2 ⫹ 3x ⫹ 1 ⫺ x) xl⬁ x l⫺⬁ x ⫺1 x6 ⫹ 1 7 21. lim xl⬁ 22. lim e ⫺x 2 xl⬁ 23. lim 共x 2 ⫺ x 4 兲 xl⬁ xl⬁ 10. lim x l ⫺⬁ xl⬁ 25. lim 9–26 Find the limit. 9. lim ■ L I M I T S AT I N F I N I T Y; H O R I Z O N TA L A S Y M P TOT E S A Click here for answers. xl⬁ LIMITS AT INFINITY; HORIZONTAL ASYMPTOTES 24. lim x3 ⫺ 1 x4 ⫹ 1 26. lim x sx ⫺ 1 xl⬁ sx ⫹ 3 x⫹3 xl⬁ 27. Guess the value of the limit lim x 2 sin xl⬁ 5 x2 by evaluating f 共x兲 苷 x 2 sin共5兾x 2 兲 for x 苷 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 50, and 100. Then confirm your guess by evaluating this limit exactly. 1 ■ SECTION 2.6 2.6 LIMITS AT INFINITY; HORIZONTAL ASYMPTOTES ANSWERS E Click here for exercises. 1. 0 8. 0 14. 3 2 20. ⫺⬁ 26. ⬁ 2. ⫺2 9. 0 3. 0 10. ⫺3 15. 0 21. ⬁ 16. 0 22. 0 4. S Click here for solutions. 7 2 5. 1 6 6. 11. 2 12. ⫺ 17. 0 18. ⫺ 23. ⫺⬁ 1 2 1 4 1 2 24. 0 7. 0 13. ⫺1 19. ⬁ 25. 0 27. 5 Stewart: Calculus: Early Transcendentals, Seventh Edtion. ISBN: 0538497904. © 2012 Cengage Learning. All rights reserved. 2
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