How often Limits and continuity is asked

Where it was asked

• Oct/Nov 202412 marks
• Oct/Nov 202314 marks
• Supp 202218 marks

The questions

1. Oct/Nov 2024, Q4.12 marks

   Evaluate the limit as x approaches 2 of the product (sin(x^2) + x) multiplied by (3e^{x^3} + 6).

2. Oct/Nov 2024, Q4.22 marks

   Evaluate the limit as u approaches π of the square root of (u^3 + 3u^4 + 6 + cos(u)).

3. Oct/Nov 2024, Q4.3.13 marks

   Let f(x) = (x^2 - 4) / |x - 2|. Find the left-hand limit of f(x) as x approaches 2 from below (x → 2⁻).

4. Oct/Nov 2024, Q4.3.22 marks

   Let f(x) = (x^2 - 4) / |x - 2|. Find the right-hand limit of f(x) as x approaches 2 from above (x → 2⁺).

5. Oct/Nov 2024, Q4.3.33 marks

   Let f(x) = (x^2 - 4) / |x - 2|. Discuss whether the limit of f(x) as x approaches 2 exists, giving reasons based on the one-sided limits found previously.