 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2001/paper-2/12/a/i/solution

Using the standard sine limit

sin t / t \to 1

x \to 0 lim \frac{sin 2 x}{x} = 2 x \to 0 lim \frac{sin 2 x}{2 x} = 2.

Thus the two-sided limit exists and is finite.

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