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GATE | GATE 2017 MOCK II | Question 34

  • Last Updated : 14 Feb, 2018

limit

(A) e
(B) e2
(C) e1/2
(D) 1


Answer: (B)

Explanation: Let,f(x) = (1 + x)^\frac{2}{sinx}
If you substitute the value of x, the value of f(x) will be in the form of 1^\infty
The limit value for the type of expressions P^Q is equals to e^{Q(P-1)}
Here, for lim_{x->0} (1+x)^{\frac{2}{sinx}}
e^{lim_{x->0} \frac{2}{sinx}(1+x-1)}
e^{lim_{x->0}2*(\frac{x}{sinx})}
We know that the value of lim_{x->0}\frac{x}{sinx}=1
The resultant value is equal to e^2


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