plumiLimits and L'Hospital's rule: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on E.6 Limits and L'Hospital's rule, 2019–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 7 questions on Limits and L'Hospital's rule, as a list
- June 2025, Paper 1, Q3 (1 mark): Which one of the following expressions cannot be evaluated by l’Hôpital’s rule? Circle your answer. [1 mark] ( ) e 2 0 0 0 0 tanh 1 lim lim lim cos sin 2 ln lim
- June 2024, Paper 1, Q4 (1 mark): Which one of the following statements is correct? Tick () one box. [1 mark] lim x 0(x2 ln x) = 0 lim x 0(x2 ln x) = 1 lim x 0(x2 ln x) = 2 lim x 0(x2 ln x) is
- June 2023, Paper 1, Q13 (5 marks): Use l’Hoˆ pital’s rule to prove that lim x ! x sin 2x cos x 2 0 B @ 1 C A = −4 [5 marks]
- June 2023, Paper 2, Q2 (1 mark): Which one of the expressions below is not equal to zero? Circle your answer. [1 mark] lim x ! 1(x2e−x) lim x ! 0(x5 ln x) lim x ! 1 ex x5 lim x ! 0(x3ex)
- June 2022, Paper 2, Q8 (10 marks): (a) The function f is defined as f (x) = sec x 8 (a) (i) Show that f (4)(0) = 5 [4 marks] 8 (a) (ii) Hence find the first three non-zero terms of the Maclaurin
- November 2021, Paper 1, Q9 (4 marks): Use l’Hoˆ pital’s rule to show that lim x ! 1(xe−x) = 0 Fully justify your answer. [4 marks]
- November 2020, Paper 2, Q11 (8 marks): (a) Starting from the series given in the formulae booklet, show that the general term of the Maclaurin series for sin x x × cos x is (×1)r+1 2r (2r + 1)!x2r [4
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