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Answer 1 · 2017-12-29T13:54:05

see below

#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)#