Limits using Maclaurin series and L'Hopital's ruleAQA A-Level Further Maths: Mind map

Exam questions on Limits using Maclaurin series and L'Hopital's rule

1. Let $L=\lim_{x\to0}\dfrac{1-\cos2x}{x^2}$.
   Use the Maclaurin series for $\cos x$ to find the value of $L$.2 marks
2. Let $M=\lim_{x\to\infty}\dfrac{x^2}{\mathrm{e}^{x}}$.
   Show how applying l'Hôpital's rule twice gives your answer to (b).2 marks
3. Let $F(x)=\dfrac{\sin x-x\cos x}{x^3}$ for $x\ne0$.
   Use Maclaurin series to find $\lim_{x\to0}F(x)$.3 marks