Question Detail
Question
Evaluate lim(x→2) (x³-64)/(x-4)... [as x approaches 4] i.e. lim(x→4) (x³-64)/(x-4)
Correct Answer
Option D is the correct answer.
Detailed Explanation
Factor x³-64=(x-4)(x²+4x+16). Cancelling (x-4), the limit becomes x²+4x+16 at x=4, which is 16+16+16=48.
Hint
Factor the numerator as a difference of cubes to cancel the (x-4) term.