Thursday, 7 July 2016

Why is the limit as x approaches 0 of fracsin(5x)x=5?.

Why is lim? 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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real analysis - How to find lim_{hrightarrow 0}frac{sin(ha)}{h}

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}...