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$\lim\limits_{x\to \infty}\big(\large\frac{x+a}{x+b}\big)^{x+b}$=

$(a)\;1\qquad(b)\;e^{b-a}\qquad(c)\;e^{a-b}\qquad(d)\;e^b$

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$\lim\limits_{x\to \infty}\big(\large\frac{x+a}{x+b}\big)^{x+b}=$$\lim\limits_{x\to \infty}\big(1+\large\frac{a-b}{a+b}\big)^{x+b}$
$\Rightarrow \lim\limits_{x\to \infty}\bigg[\big(1+\large\frac{a-b}{x+b}\big)^{\Large\frac{x+b}{a-b}}\bigg]^{a-b}$
$\Rightarrow e^{a-b}$
Hence (c) is the correct answer.
answered Dec 24, 2013 by sreemathi.v
 
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