Evaluate lim x→√3 ( x^2 - 3 )/( x^2 + 3√3x - 12)
( Without using L'Hopital's rule )
( Without using L'Hopital's rule )
-
lim ( x^2 - 3 )/( x^2 + 3√3x - 12) when x→√3
= lim ( x - √3 ) (x +√3) /( x-√3) (x +4√3)
= lim (x +√3) / (x +4√3) when x→√3
= lim 2 √3 / 5 √3 when x→√3
= 2/5
answer
= lim ( x - √3 ) (x +√3) /( x-√3) (x +4√3)
= lim (x +√3) / (x +4√3) when x→√3
= lim 2 √3 / 5 √3 when x→√3
= 2/5
answer