How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule?
I know when I use lhopital I easy get
$$ \lim_{h\rightarrow 0}\frac{\cos(ah)a}{1} = a$$ but I don't know how to behave without that way
Answer
Hint:
$$\frac{\sin(ha)}{h} = a\cdot\frac{\sin(ha)}{ha}$$
Also, remember what $$\lim_{x\to 0}\frac{\sin(x)}{x}$$ is equal to?
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