#lim_(x rarr 1) (x^3+x)/(x(x-1))# ?

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Answer 1 · 2018-01-19T12:12:02

Undefined

#(x^3+x)/(x(x-1)#

#(x(x^2+1))/(x(x-1))#

#(cancelx(x^2+1))/(cancelx(x-1))#

#(x^2+1)/(x-1)=(x^2+1)*1/(x-1)#

#color(green)(lim_(x->a)f(x)*g(x)=lim_(x->a)f(x) *lim_(x->a)g(x)#

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

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

#lim_(x->1^-)(1/(x-1))=-oo#

#lim_(x->1^+)(1/(x-1))!=lim_(x->1^-)(1/(x-1))#

#:.#

#lim_(x->1)((x^3+x)/(x(x-1)))color(white)(888)#Undefined