Evaluate the limit lim as x-->2 arctan((x^2-4)/(3x^2-6x))
lim (x -> 2) { arctan[ (x^2 - 4) / (3x^2 - 6x) ] }
= lim (x -> 2) { arctan[ (x - 2)(x + 2) / 3x(x - 2) ] }
= lim (x -> 2) { arctan[ (x + 2) / (3x) ] }
= lim (x -> 2) { arctan[ 4 / 6 ] }
= arctan(2 / 3).
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lim (x -> 2) { arctan[ (x^2 - 4) / (3x^2 - 6x) ] }
= lim (x -> 2) { arctan[ (x - 2)(x + 2) / 3x(x - 2) ] }
= lim (x -> 2) { arctan[ (x + 2) / (3x) ] }
= lim (x -> 2) { arctan[ 4 / 6 ] }
= arctan(2 / 3).