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

 \\ \lim_{x\to \infty } x^{\frac{1}{x}} is
(A)
(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   )

ln(m)=0

m=e0=1

 

 

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