SOLUTION: Please evaluate : Lim x tends to zero, ((tanx)/x)^(1/x^2) with step by step solution. The answer is = e^(1/3) as per book. Regard Khoka123

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please evaluate : Lim x tends to zero, ((tanx)/x)^(1/x^2) with step by step solution. The answer is = e^(1/3) as per book. Regard Khoka123      Log On


   

Question 890090: Please evaluate :
Lim x tends to zero, ((tanx)/x)^(1/x^2) with step by step solution. The answer is = e^(1/3) as per book.
Regard
Khoka123
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Exponentiate:



Using the fact that is continuous at and if is continuous around and is continuous around , then



Use a Taylor Series expansion at to compute



Hence,



John

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