Why is $\lim\limits_{x \to 0} \frac{\sin(5x)}{x} = 5$? Is there some trig identity according to which $\sin(cx) = c\cdot\sin(x)$ (or any identity that could help solve this problem)? I already know that $\lim\limits_{x \to 0} \frac{\sin(x)}{x} = 1$, but I'm not sure exactly how to proceed in this particular case. Thanks in advance.
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