Prove that lim In(x) = -. X 0+ Given N? 0 we need 8 > 0...

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Prove that lim In(x) = -∞. X→→ →0+ Given N? 0 we need 8 > 0 so that In(x) ---Select--- ◊ whenever 0 < x < ? ✨ ; that is, x = eln(x) ? ✨ eN whenever 0<x< ? ✨ . This suggests that we take 8 = e. If 0 < x < eN, then In(x) ? ✨ In(e) = N. By the definition of a limit, lim In(x) = -00. x →0+ Prove that lim In(x) = -∞. X→→ →0+ Given N? 0 we need 8 > 0 so that In(x) ---Select--- ◊ whenever 0 < x < ? ✨ ; that is, x = eln(x) ? ✨ eN whenever 0<x< ? ✨ . This suggests that we take 8 = e. If 0 < x < eN, then In(x) ? ✨ In(e) = N. By the definition of a limit, lim In(x) = -00. x →0+

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We use the limit definition The given question ... View the full answer