Moderate -0.5 This is a standard limit question testing knowledge of indeterminate forms and L'Hôpital's rule or growth rate comparison. While it requires recognizing that x² dominates ln x as x→0⁺, making the limit 0, this is a routine Further Maths concept presented as a straightforward multiple-choice question worth only 1 mark, making it easier than average.
Which one of the following statements is correct?
Tick ($\checkmark$) one box.
[1 mark]
$\lim_{x \to 0}(x^2 \ln x) = 0$ $\square$
$\lim_{x \to 0}(x^2 \ln x) = 1$ $\square$
$\lim_{x \to 0}(x^2 \ln x) = 2$ $\square$
$\lim_{x \to 0}(x^2 \ln x)$ is not defined. $\square$
\hfill \mbox{\textit{AQA Further Paper 1 2024 Q4 [1]}}