A) 1
B) 1/2
C) 0
D) None of these
Correct Answer: A
Solution :
[a] As f is continuous. \[f(0)=\underset{x\to 0}{\mathop{\lim }}\,f(x)=\underset{n\to \infty }{\mathop{\lim }}\,f(1/4n)\] \[=\underset{n\to \infty }{\mathop{\lim }}\,\left( (\sin \,\,{{e}^{n}}){{e}^{-{{n}^{2}}}}+\frac{1}{1+1/{{n}^{2}}} \right)=0+1=1\].
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