Question Number 101096 by student work last updated on 30/Jun/20

find the oblique asymptote of f(x)=x∙e^(1/x)         i need your help

Commented bystudent work last updated on 30/Jun/20

i need soon

Commented bystudent work last updated on 30/Jun/20

who can help me?

Answered by mathmax by abdo last updated on 30/Jun/20

lim_(x→+∞) f(x) =lim_(x→+∞)  xe^(1/x)  =lim_(x→+∞) x =+∞  lim_(x→+∞)  ((f(x))/x) =lim_(x→+∞)  e^(1/x)  =1  lim_(x→+∞) f(x)−x =lim_(x→+∞) x e^(1/x) −x =lim_(x→+∞) x(e^(1/x) −1) but  e^(1/x)  =1+(1/x) +o((1/x^2 )) ⇒e^(1/x) −1 =(1/x)+o((1/x^2 )) ⇒x(e^(1/x) −1) =1+o((1/x)) ⇒  lim_(x→+∞) f(x)−x =1 ⇒the line y =x+1 is oblique assymptote  to C_f  at +∞  same result at −∞