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If $\lim\limits_{x\to \infty}\big(1+\large\frac{a}{x}+\frac{b}{x^2}\big)^{2x}$$=e^2$ then the value of a and b are

$\begin{array}{1 1}(a)\;a\in R,b\in R&(b)\;a=1,b\in R\\(c)\;a\in R,b=2&(d)\;a=1\;and\;b=2\end{array}$

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$\lim\limits_{x\to \infty}\big(1+\large\frac{a}{x}+\frac{b}{x^2}\big)^{2x}$$=e^2$
$\Rightarrow e^{\Large\lim\limits_{x\to \infty}\big(\Large\frac{a}{x}+\frac{b}{x^2}\big)^{2x}}$$=e^2$
$\Rightarrow e^{2a}=e^2$
$\Rightarrow a=1,b\in R$
Hence (b) is the correct answer.
answered Jan 6, 2014 by sreemathi.v
 

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