How can I solve that without using L'Hôpital's rule (which is considered illegal in my calculus class)?
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For small x (which we have here, since we're letting x tend to 0) you can use the first order Taylor expansion for sin(x) which is x. So for small x: It's also possible that you have to use the 'standard limit': In that case, rewrite as follows:
Cinder I realize that this is off topic. I looked at your LaTex code an saw that you wrote that limit in array mode. I think it is easier if you write it as: \lim_{n\to 0}\frac{\sin 2x}{\sin 3x}
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