If a, b, c and d are positive then `lim_(x to oo)(1+(1)/(a+bx))^(x+dx)` is eqqual

Options

A. `e^(d//b)`
B. `e^(c//a)`
C. `e^((c+d)//(a+b))`
D. e

Answer

A

Explanation

`L=underset(xtooo)lim(1+(1)/(a+bx))^(c+dx)" "["from"(1)^(oo)]`
`=e^(underset(x tooo)lim(c+dx)/(a+bx))=e^(underset(x tooo)lim(c//x+d)/(a//x+b))`
`=e^((0+d)/(0+d))=e^(d//b)`