A) \[{{e}^{d/b}}\]
B) \[{{e}^{c/a}}\]
C) \[{{e}^{(c+d)/(a+b)}}\]
D) \[e\]
Correct Answer: A
Solution :
\[\underset{x\to \infty }{\mathop{\lim }}\,\,{{\left( 1+\frac{1}{a+bx} \right)}^{c+dx}}=\underset{x\to \infty }{\mathop{\lim }}\,\,{{\left\{ {{\left( 1+\frac{1}{a+bx} \right)}^{a+bx}} \right\}}^{\frac{c+dx}{a+bx}}}={{e}^{d/b}}\] \[\left\{ \because \,\,\underset{x\to \infty }{\mathop{\lim }}\,\,{{\left( 1+\frac{1}{a+bx} \right)}^{a+bx}}=e \right.\]and \[\left. \underset{x\to \infty }{\mathop{\lim }}\,\frac{c+dx}{a+bx}=\frac{d}{b} \right\}\].
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