Find the limits in Exercises 51-66. 51. limx⇒1+x11−x 52. limx⇒1+x11−x 53. limx⇒∞(ln⁡x)1x 54. limx⇒e+(ln⁡x)1x−e 55. limx⇒0+x−1ln⁡x 56. limx⇒∞x1ln⁡x 57. limx⇒∞(1+2x)12ln⁡x 58. limx⇒0(ex+x)1x 59. limx⇒0+xx 60. limx⇒0+(1+1x)x 61. limx⇒0(x+2x−1)x 62. limx⇒∞(x2+1x+2)1x 63. limx⇒0+x2ln⁡x 64. limx⇒0+x(ln⁡x)2 65. limx⇒0+xtan⁡(π2−x) 66. limx⇒0+sin⁡x⋅ln⁡x

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Find the limits in Exercises 51-66.  51. limx⇒1+x11−x                                52. limx⇒1+x11−x   53. limx⇒∞(ln⁡x)1x                               54. limx⇒e+(ln⁡x)1x−e  55. limx⇒0+x−1ln⁡x                                             56. limx⇒∞x1ln⁡x  57. limx⇒∞(1+2x)12ln⁡x       58. limx⇒0(ex+x)1x  59. limx⇒0+xx                                                       60. limx⇒0+(1+1x)x  61. limx⇒0(x+2x−1)x                        62. limx⇒∞(x2+1x+2)1x  63. limx⇒0+x2ln⁡x                                                64. limx⇒0+x(ln⁡x)2  65. limx⇒0+xtan⁡(π2−x)                  66. limx⇒0+sin⁡x⋅ln⁡x

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Find the limits in Exercises 51-66.  51. limx⇒1+x11−x                                52. limx⇒1+x11−x   53. limx⇒∞(ln⁡x)1x                               54. limx⇒e+(ln⁡x)1x−e  55. limx⇒0+x−1ln⁡x                                             56. limx⇒∞x1ln⁡x  57. limx⇒∞(1+2x)12ln⁡x       58. limx⇒0(ex+x)1x  59. limx⇒0+xx                                                       60. limx⇒0+(1+1x)x  61. limx⇒0(x+2x−1)x                        62. limx⇒∞(x2+1x+2)1x  63. limx⇒0+x2ln⁡x                                                64. limx⇒0+x(ln⁡x)2  65. limx⇒0+xtan⁡(π2−x)                  66. limx⇒0+sin⁡x⋅ln⁡x

Find the limits in Exercises 51-66. 51. \lim_{x \Rightarrow 1^{

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