Tuesday 1 October 2019

calculus - If a function such that $f(x+y)=f(x)+f(y)$ is continuous at $0$, then it is continuous on $mathbb R$

Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a function such that $f(x+y)=f(x)+f(y)$. If $f$ is continuous at zero how can I prove that is continuous in $\mathbb{R}$.

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real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

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