Evaluate lim_(x -> 7) (x^2 - 49) / (x - 7).
Answer and explanation
Correct answer: D. 14
- Step 1: Direct substitution gives 0/0, so factorise: x^2 - 49 = (x - 7)(x + 7).
- Step 2: Cancel (x - 7): the limit becomes lim (x + 7) as x -> 7.
- Step 3: Substitute: 7 + 7 = 14.
Answer
14.
Why not the others: '7' gives the value of k instead of the sum k + k; '49' substitutes x = 7 into the numerator only; '0' treats the 0/0 form as equal to zero instead of simplifying.
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