Question Detail
Question
Evaluate lim(x→2) (x⁶-64)/(x³-8)
Correct Answer
Option C is the correct answer.
Detailed Explanation
Both numerator and denominator factor with (x³-8) as a common term: x⁶-64=(x³-8)(x³+8). Cancelling leaves x³+8, which at x=2 gives 8+8=16.
Hint
Recognise x⁶-64 as a difference of squares in terms of x³, sharing a factor with the denominator.