Find the limit #lim_(x->1)(sqrt(x^2-1)+sqrt(x+1))/sqrt(x^3-1)#?

1 Answer
Shwetank Mauria
Jan 28, 2018

#lim_(x->1)(sqrt(x^2-1)+sqrt(x+1))/sqrt(x^3-1)=oo#

Explanation:

#lim_(x->1)(sqrt(x^2-1)+sqrt(x+1))/sqrt(x^3-1)#

= #lim_(x->1)(sqrt(x^2-1))/sqrt(x^3-1)+lim_(x->1)sqrt(x+1)/sqrt(x^3-1)#

= #lim_(x->1)sqrt((x+1)(x-1))/sqrt((x-1)(x^2+x+1))+lim_(x->1)sqrt(x+1)/sqrt(x^3-1)#

= #lim_(x->1)sqrt(x+1)/sqrt(x^2+x+1)+lim_(x-1)sqrt(x+1)/sqrt(x^3-1)#

= #sqrt2/sqrt3+oo#

= #oo#

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