Evaluate lim_(x -> 5) (x^2 - 25) / (x - 5).
Answer and explanation
Correct answer: D. 10
- Step 1: Direct substitution gives 0/0, so factorise: x^2 - 25 = (x - 5)(x + 5).
- Step 2: Cancel (x - 5): the limit becomes lim (x + 5) as x -> 5.
- Step 3: Substitute: 5 + 5 = 10.
Answer
10.
Why not the others: '5' gives the value of k instead of the sum k + k; '25' substitutes x = 5 into the numerator only; '0' treats the 0/0 form as equal to zero instead of simplifying.
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