Question Number 149700 by Lekhraj last updated on 06/Aug/21

Commented byiloveisrael last updated on 07/Aug/21

lim_(x→−∞) (x+x(√(1+4x^(−1) ))) = lim_(x→−∞) x(1+(√(1+4x^(−1) )) ) =−∞×2 = −∞

Answered by MJS_new last updated on 06/Aug/21

(√(x^2 +4x))>0 if x<−4 ⇒ very obviously the limit is −∞

Answered by ajfour last updated on 06/Aug/21

L=lim_(y→∞) ((4y)/( (√(y^2 −4y))−y)) =lim_(y→∞) (4/( (√(1−(4/y)))−1)) =lim_(y→∞) (4/(1−(2/y)−1))= −∞