Menu Close

lim-x-1-1-x-x-2-e-x-

Tinku Tara 0 Comments
Pin




Question Number 118950 by benjo_mathlover last updated on 21/Oct/20
lim_(x→∞) (1+(1/x))^x^2 .e^(−x) = ?.
limx→∞(1+1x)x2.e−x=?.
Answered by john santu last updated on 21/Oct/20
L = lim_(x→∞) (((1+(1/x))^x^2 )/e^x ) ln L= lim_(x→∞) ln ((((1+(1/x))^x^2 )/e^x )) ln L = lim_(x→∞) x^2 (ln (1+(1/x))−x) [ by using Maclaurin series ] ln L = lim_(x→∞) x^2 ((1/x)−(1/(2x^2 ))+(1/(3x^3 ))−O(x^3 ))−x) ln L = lim_(x→∞) [x−(1/(2x))+(1/(3x^2 ))−O(x^2 )−x ] ln L = lim_(x→∞) (−(1/2)+(1/(3x^2 ))−O(x^2 ))=−(1/2) L = e^(−(1/2)) = (1/( (√e))) .
L=limx→∞(1+1x)x2exlnL=limx→∞ln((1+1x)x2ex)lnL=limx→∞x2(ln(1+1x)−x)[byusingMaclaurinseries]lnL=limx→∞x2(1x−12x2+13x3−O(x3))−x)lnL=limx→∞[x−12x+13x2−O(x2)−x]lnL=limx→∞(−12+13x2−O(x2))=−12L=e−12=1e.

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *