Evaluate `lim_(xtooo) (1+(1)/(a+bx))^(c+dx)` , where a, b, c, and d are positive.

Options

A. 4
B. 2
C. -1
D. 0

Answer

`e^(d//b)`

Explanation

`underset(xtooo)lim(1+(1)/(a+bx))^(c+dx)=underset(xtooo)lim{(1+(1)/(a+bx))^(a+bx)}^((c+dx)/(a+bx))=e^(d//b)`
`{becauseunderset(xtooo)lim(1+(1)/(a+bx))^(a+bx)=e" and "underset(xtooo)lim(c+dx)/(a+bx)=d/b}`