Evaluate `lim_(x rarr 2) [(x^(2) - 5x + 6)/(x^(2) - 3x + 2)]`.

1.	Evaluate `lim_(x rarr 2) [(x^(2) - 5x + 6)/(x^(2) - 3x + 2)]`.
Answer» When `x = 2, (4 -10 + 6)/(4 - 6 + 2)=(0)/(0)`, which is an indeterminate form. Now, `x^(2) - 5x + 6 = (x-3)(x-2)` `x^(2) - 3x + 2 = (x-1)(x-2)` `" "underset(x rarr 2)("lim")[(x^(2) - 5x + 6)/(x^(2) - 3x + 2)]=underset(x rarr 2)("lim")[((x-3) (x-2))/((x-1) (x-2))]` `" "underset(x rarr 2)("lim")[(x-3)/(x-1)]=[(2-3)/(2-1)]= -1`.

Discussion

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