Question Number 149346 by Study last updated on 04/Aug/21

lim_(x→∞) (((3x+12)/(6x−20)))^(2x) =?

Commented byStudy last updated on 04/Aug/21

helpe me

Answered by gsk2684 last updated on 04/Aug/21

lim_(x→∞) ((3x+12)/(6x−20))=lim_(x→∞) ((3+((12)/x))/(6−((20)/x)))=((3+0)/(6−0))=(1/2)<1 then lim_(x→∞) (((3x+12)/(6x−20)))^(2x) =((1/2))^∞ =0

Answered by puissant last updated on 04/Aug/21

=lim_(x→∞) e^(2xln(((3x+12)/(6x−20)))) =lim_(x→∞) e^(2xln(((3+((12)/x))/(6−((20)/x))))) =lim_(x→∞) e^(2xln((1/2))) =lim_(x→∞ ) e^(−2xln2) = { ((+∞ if x→−∞)),((0 if x→+∞)) :}