Evaluate the limit of the fraction (x^2-4)/(x^2+x-6) as x approaches to 2.

Expert Answers

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We have to find: lim x-->2 [(x^2-4)/(x^2+x-6)]

substituting x= 2 gives the indeterminate form 0/0. So we can substitute the numerator and the denominator with their derivatives using l'Hopital's rule.

=> lim x-->2 [ 2x / (2x + 1)]

Substitute x = 2

=> 4/ 5

The required value of lim x-->2 [(x^2-4)/(x^2+x-6)] = 4/5

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