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CSS Pure Mathematics QUESTION #1263
Question 1
Using the epsilon-delta definition, \(\lim_{x\to 2}\dfrac{x^3-4}{x^2+1}\) equals:
  • \(\dfrac{2}{5}\)
  • \(\dfrac{4}{5}\)✔️
  • \(\dfrac{8}{5}\)
  • \(1\)
Correct Answer Explanation
Direct substitution: \(\dfrac{(2)^3-4}{(2)^2+1}=\dfrac{8-4}{4+1}=\dfrac{4}{5}\). The function is continuous at \(x=2\), so the limit equals the function value.