Let $X$ be a random variable with cumulative distribution function $F(x)$. Then how to rigorously prove the following two limit statements?
$\lim_{x \to - \infty} F(x) = 0$.
$\lim_{x \to + \infty} F(x) = 1$.
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}...
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