Solve the following limits 13. lim (7* - 5*) 14. lim (72x - 27x) 896 15. lim

Solve the following limits 

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13. lim (7* - 5*) 14. lim (72x - 27x) 896 15. lim x0+ 16. lim ( ( + - Section 32. Indeterminate Forms and L'Hpital's Rule 17. lim (2) 1 ex sin(x) (+---+-) ex 1 18. lim (log, (x) - log(x)) X48 19. lim (log(x) -log(x)) x+0+ 20. lim (2x) x+0+ 21. lim x* x-0+ 2x 22. lim In(x + 1) x+0+ 24. lim x x0+ 26. lim x+0+ 23. lim (ln(x + 1)) n x+0+ -In(x+1) 25. lim xln(x+1) x-0+ x 27. lim x/x x -log3 (x+1) VI +0+x 28. lim(1/x) sin(2/x) 5x 29. lim (2x + 3 ) X18 2x - 2x 30. lim (3x=1)x - + 4 In(x+1) 31. lim(3x + 5x) 1/x X 32. lim (3* +5*) 1/x 33. lim (3x + 5x) 1/x 1 34. lim (3x + 5x) 1/x x-0- The next three problems are loose ends from Section 29. The limits will tell us the horizontal asymptote of each function, and in which direction. 35. lim (3x-8)ex/4 and lim (3x - 8) ex/4 X41X X 36. lim (2x + 7)e-2x/3 and lim (2x + 7)e-2x/3 X- 37. lim [5ex/3 - 7ex/4] and lim [5ex/ 7ex/4]. X118 X48 1 38. Show that lim = for all p > 0 and k > 0. ekx x+0 XP Start with p being a positive integer, then think about what happens if p is an arbitrary positive number, such as p = 7. 13. lim (7* - 5*) 14. lim (72x - 27x) 896 15. lim x0+ 16. lim ( ( + - Section 32. Indeterminate Forms and L'Hpital's Rule 17. lim (2) 1 ex sin(x) (+---+-) ex 1 18. lim (log, (x) - log(x)) X48 19. lim (log(x) -log(x)) x+0+ 20. lim (2x) x+0+ 21. lim x* x-0+ 2x 22. lim In(x + 1) x+0+ 24. lim x x0+ 26. lim x+0+ 23. lim (ln(x + 1)) n x+0+ -In(x+1) 25. lim xln(x+1) x-0+ x 27. lim x/x x -log3 (x+1) VI +0+x 28. lim(1/x) sin(2/x) 5x 29. lim (2x + 3 ) X18 2x - 2x 30. lim (3x=1)x - + 4 In(x+1) 31. lim(3x + 5x) 1/x X 32. lim (3* +5*) 1/x 33. lim (3x + 5x) 1/x 1 34. lim (3x + 5x) 1/x x-0- The next three problems are loose ends from Section 29. The limits will tell us the horizontal asymptote of each function, and in which direction. 35. lim (3x-8)ex/4 and lim (3x - 8) ex/4 X41X X 36. lim (2x + 7)e-2x/3 and lim (2x + 7)e-2x/3 X- 37. lim [5ex/3 - 7ex/4] and lim [5ex/ 7ex/4]. X118 X48 1 38. Show that lim = for all p > 0 and k > 0. ekx x+0 XP Start with p being a positive integer, then think about what happens if p is an arbitrary positive number, such as p = 7.