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 [AIEEE 2004]

If \[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( 1+\frac{a}{x}+\

1.	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 [AIEEE 2004]
A.	\[a=1,\ b=2\]
B.	\[\cos (\|x\|)\,-\|x\|\]
C.	\[a\in R,\ b=2\]
D.	\[a\in R,\ b\in R\]
Answer» C. \[a\in R,\ b=2\]

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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 [AIEEE 2004]

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