Question

How do you determine the limit of `(3/x^3) ((x-2)/(x-1))` as x approaches 1-?

Answer 1

`lim_(xrarr1^(-))3/x^3*((x-2)/(x-1))=-oo`

Explanation:

`lim_(xrarr1^(-))(3(x-2))/(x^3(x-1))=`

`lim_(xrarr1^(-))3/x^3*((x-2)/(x-1))=-oo`

because

`x->1^-` `<=>` `x-1<0` so `lim_(xrarr1^(-))1/(x-1)=^((1/0^(-)))=-oo`