Limits using Maclaurin series and L'Hopital's rule

Limits using Maclaurin series and L'Hopital's rule Quiz

Spec D7 · AQA A-Level Further Maths: Quiz

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5 questions, one answer each

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1. What is $\lim_{x\to0}\frac{\mathrm{e}^x-1}{x}$ ?
- A. $0$
- B. $1$
- C. $\infty$
- D. $\mathrm{e}$
2. What is $\lim_{x\to0}\frac{1-\cos x}{x^2}$ ?
- A. $0$
- B. $1$
- C. $2$
- D. $\frac12$
3. What is $\lim_{x\to\infty}\frac{\ln x}{x}$ ?
- A. $0$
- B. $1$
- C. $\infty$
- D. $\mathrm{e}$
4. What is $\lim_{x\to0}\frac{\sin3x}{\sin5x}$ ?
- A. $1$
- B. $\frac53$
- C. $\frac35$
- D. $0$
5. Which condition must hold before applying l'Hôpital's rule?
- A. $f(a)\ne0$
- B. $g'(a)=0$
- C. $f$ and $g$ are polynomials
- D. the limit has the form $\frac00$ or $\frac{\infty}{\infty}$