Evaluate the limit: lim (x -> 3) [ (x^2 - 9) / (x - 3) ].
Answer and explanation
Correct answer: D. 6
- Step 1: Factor the numerator as a difference of two squares: x^2 - 9 = (x - 3)(x + 3).
- Step 2: Cancel the common non-zero factor (x - 3) for x != 3: lim (x -> 3) (x + 3) = 3 + 3 = 6.
Answer
6.
Why not the others: '0' results from erroneously substituting into the numerator without dividing out the factor; '3' substitutes into only one term; 'Undefined' overlooks algebraic cancellation of the removable discontinuity.
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