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GATE | GATE-CS-2015 (Set 1) | Question 65

  • Difficulty Level : Basic
  • Last Updated : 14 Feb, 2018

 \\ \lim_{x\to \infty } x^{\frac{1}{x}} is
(B) 0
(C) 1
(D) Not Defined

Answer: (C)

Explanation: \lim_{x\to\infty} 1/x

= 0. and

\lim_{x\to\infty} x^0

= 1.


Alternate method : Using log

lnm=lim x->infinity 1/x*lnx

lim x->infinity lnx/x  (numerator = finite value,denominator = infinity and finite/infinite=0   )





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