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Quiz

Year 4: Limits of functions

10 questions with solutions for year 4: limits, the forms 0/0 and ∞/∞, special limits, asymptotes – review problems.

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

1. Find the limit: lim (x³ − 5x + 7), x → −2

2. Find the limit: lim (5x − 7)/(3x + 2), x → 4

3. Find the limit: lim (x² − 3x)/(x² − 9), x → 3

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

5. Find the limit: lim (x⁴ − 16)/(2x² + 4x − 16), x → 2

6. Find the limit: lim (√(x + 4) − 2)/x, x → 0

7. Find the limit: lim (2x³ − 7x + 4)/(3x³ + 3x² − x), x → ∞

8. Find the limit: lim sin 7x / sin 4x, x → 0

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

10. Asymptotes of f(x) = 3x/(x + 1):