Find the limits in Exercises 51–66. 51. lim x'/(1-x) x-1+ 52. lim x'/x-1) x→1+ 53. lim (In x)'/x 54. lim (In x)/x-e) х—е 55. lim x1/In x x→0* 56. lim x'/In x 57. lim (1 + 2x)'/(2 In x) 58. lim (e* + x)'/x 60. lim ( 1 + x→0+ 59. lim x* x→0* 1/x x² + 1 61. lim 62. lim x0x + 2 lim x(ln x)² x→0* 63. lim x² In x 64. x→0* 66. lim sin x • In x x→0+ 65. lim x tan x→0+

Q: Find the limit

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Q: lim In x X-→ 0+

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A: Given query is to find indicated limit.

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A: Obtain the value of the limit as follows.

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A: Given :          limx→0+1ex-1-1x

Q: if x ‡ 4; if x = 4. Find limx→4 f(x) where ƒ is given above, show all of your work. 10. Let f(x) = {…

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A: For simplification divide the numerator and the denominator by x, and then apply the limit as x…

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Q: 1 x-1 x-1 ln x 3) lim

A: Explanation of the answer is as follows