(Solved): In Problems 25-32, use L'Hpital's rule to find the limit. Note that in these problems, neither alg ...

In Problems 25-32, use L'Hôpital's rule to find the limit. Note that in these problems, neither algebraic simplification nor Theo- rem 4 of Section 9.2 provides an alternative to L'Hôpital's rule. 25. lim x-0 4x 27. lim 29. lim x?? 31. lim et - 1 X x? In x² 33. lim x 1 In x² 35. lim x+5x+4 x³ + 1 x + 2 2(x-2)4 x 1 *1 ln x³ In Problems 33-36, explain why L'Hôpital's rule does not apply. If the limit exists, find it by other means. e4x14x 1² 26. lim 37. lim- x->0 3x x0e¹-1 28. lim 30. lim x ln x 32. lim 34. lim x?? ln x +² x3 (x + 3) 5 Find each limit in Problems 37-60. Note that L'Hôpital's rule does not apply to every problem, and some problems will require more than one application of L'Hôpital's rule. 36. lim 3x + 1 - ³x 1² 38. lim- x-0