question_answer

If\[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( 1+\frac{a}{x}+\frac{b}{{{x}^{2}}} \right)}^{2x}}={{e}^{2}},\]then the values of a and b are

A) \[a\in R,b\in R\]   

B)        \[a=1,b\in R\]   

C)        \[a\in R,b=2\]   

D)        \[a=1,b=2\]

Correct Answer: B

Solution :

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