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Quiz

Year 3: Elementary functions and limits

10 questions with solutions for year 3: zeros and intercepts, monotonicity, quadratic functions, limits of sequences and functions – review problems.

Type the number or choose the right answer. When you finish, click Check answers and see the solutions.

1. Where does the graph of f(x) = ln(x² − 8) meet the x-axis?

2. For which k is f(x) = (2k + 3)x + 3 increasing?

3. The vertex of f(x) = 2x² − 4x + 5 is:

4. Find the limit: lim (2n + 1)/(n + 1), n → ∞

5. Find the limit: lim (2n − 1)/(5n + 3), n → ∞

6. Find the limit: lim √n(√(n + 1) − √n), n → ∞

7. Find the limit: lim (√(n² − 5n + 6) − n), n → ∞

8. Find the limit: lim (x − 3)/(x² − 2x − 3), x → 3

9. Find the limit: lim (x² − 2x + 1)/(x³ − x² − x + 1), x → 1

10. Find the limit: lim (1 + 2x)^(1/x), x → 0