#lim_(x->0) 1/x^2-(x-2)/(x^3-x)=# ?

1 Answer
· Cesareo R.
Dec 26, 2017

#oo#

Explanation:

#color(white)(=)lim_(x->0) 1/x^2-(x-2)/(x^3-x)#
#=lim_(x->0) 1/x^2-(x-2)/(x(x^2-1))#
Common denomiator
#=lim_(x->0) ((x^2-1)-x(x-2))/(x^2(x^2-1))#
#=lim_(x->0) (x^2-1-x^2+2x)/(x^2(x^2-1))#
#=lim_(x->0) (-1+2x)/(x^2(-1+x^2))#
#=lim_(x->0) 1/x^2(1-2x)/(1-x^2)#
#=lim_(x->0) 1/x^2 xx lim_(x->0) (1-2x)/(1-x^2) = oo xx 1 = oo#

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