Evaluate the following limit: `underset( x rarr - 2) ( "lim")(x^3+x^2+4x+12)/(x^3-3x+2)`

Explanation

Given,

`(lim)_(x->−2)(x^3+x^2+4x+12)/(x^3−3x+2)`

`=(lim)_(x->−2)((-2)^3+(-2)^2+4(-2)+12)/((-2)^3−3(-2)+2)`

`=0/0`

which has `0/0` form thus by applying l-hospital rule,


`(lim)_(x->−2)(x^3+x^2+4x+12)/(x^3−3x+2)`

`=(lim)_(x->−2)(3x^2+2x+4)/(3x^2−3)`

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