Question #e12fb

1 Answer
Dec 29, 2017

see below

Explanation:

Lim_(xrarr0)xsqrt(1+x-2)=0*sqrt(-1)...?

or

Lim_(xrarr0)x/(sqrt(1+x-2))=0/sqrt(-1).....?

or

Lim_(xrarr0)x/(sqrt(1+x)-2)=0/-1=0

or

Lim_(xrarr0)x(sqrt(1+x)-2)=0*(sqrt1-2)=0

or, infinity?

Lim_(xrarroo)x/(sqrt(1+x)-2)*(sqrt(1+x)+2)/(sqrt(1+x)+2)

Lim_(xrarroo)(x(sqrt(1+x)+2))/(1+x-4)=Lim_(xrarroo)(cancelx(sqrt(1+x)+2))/(cancelx(1-3/x))

Lim_(xrarroo)(sqrt(1+x)+2)/(1-3/x)=oo/1=oo

or, this one?

Lim_(xrarroo)x(sqrt(1+x)-2)*(sqrt(1+x)+2)/(sqrt(1+x)+2)

Lim_(xrarroo)(x(1+x-4))/(sqrt(1+x)+2)

Lim_(xrarroo)(x^2-3x)/(sqrt(1+x)+2)=oo^(3/2)-oo^(1/2)