Sunday, 21 October 2018

calculus - Why the limit of $frac{sin(x)}{x}$ as $x$ approaches 0 is 1?

I need a rigorous proof that verify why the limit of $\dfrac{\sin(x)}{x}$ as $x$ approaches $0$ is $1$.
I tried before but i do not know how start this proof.
I would appreciate if somebody help me. Thanks.

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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}...