Easy -1.8 This is a straightforward multiple-choice question testing basic limit behavior and dominance of exponential vs polynomial functions. Students need only recall that exponentials dominate polynomials and apply L'Hôpital's rule or standard limit results. The third option clearly tends to infinity while others tend to zero, making this a routine recognition task with minimal calculation required.
Which one of the expressions below is not equal to zero?
Circle your answer.
[1 mark]
\(\lim_{x \to \infty} (x^2e^{-x})\) \quad \(\lim_{x \to 0} (x^5 \ln x)\) \quad \(\lim_{x \to \infty} \left(\frac{e^x}{x^5}\right)\) \quad \(\lim_{x \to 0^+} (x^3e^x)\)
Which one of the expressions below is not equal to zero?
Circle your answer.
[1 mark]
$\lim_{x \to \infty} (x^2e^{-x})$ \quad $\lim_{x \to 0} (x^5 \ln x)$ \quad $\lim_{x \to \infty} \left(\frac{e^x}{x^5}\right)$ \quad $\lim_{x \to 0^+} (x^3e^x)$
\hfill \mbox{\textit{AQA Further Paper 2 2023 Q2 [1]}}