Browse Questions

# If $a,b,c,d$ are positive then $\lim\limits_{x\to \infty}\big(1+\large\frac{1}{a+bx}\big)^{c+dx}=$

$(a)\;e^{\large d/b}\qquad(b)\;e^{\large c/a}\qquad(c)\;e^{\large(c+d)/a+b}\qquad(d)\;e$

$\lim\limits_{x\to \infty}\big(1+\large\frac{1}{a+bx}\big)^{c+dx}$
$\Rightarrow \lim\limits_{x\to \infty}\big[\big(1+\Large\frac{1}{a+bx}\big)^{a+bx}\big]^{\Large\frac{c+dx}{a+bx}}$
$\Rightarrow \lim\limits_{x\to \infty}\big[\big(1+\Large\frac{1}{a+bx}\big)^{a+bx}\big]^{\lim\limits_{x\to \infty}\Large\frac{c+dx}{a+bx}}$
$\Rightarrow e^{d/b}$
Hence (a) is the correct answer.