 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2009/paper-1/20/b/i/solution

sin (3 x) = 3 x + O (x^{3})

and

sinh x = x + O (x^{3})

. Dividing by

x

in a punctured neighborhood of zero gives

x \to 0 lim \frac{sin ( 3 x )}{sinh x} = 3.

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