 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-1/19/d/i/solution

Write the product as a quotient with indeterminate form

(- \infty) / (+ \infty)

lim_{x \to 0^{+}} x ln x = lim_{x \to 0^{+}} \frac{l n x}{1/ x} = lim_{x \to 0^{+}} \frac{1/ x}{- 1/ x ^{2}} = lim_{x \to 0^{+}} (- x) = 0 .

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