show its continuity

**flyingsquirrel** · May 17th 2008, 01:05 PM

Hi

For the continuity of $f$ , we know that $\lim_{h\to0}f(x_0+h)=f(x_0)$ and we want $\forall y\in\mathbb{R},\, \lim_{h\to0}f(y+h)=f(y)$ . You may try to write $\lim_{h\to 0}f(y+h)=\lim_{h\to0} f(y-x_0+x_0+h)=\ldots$

For the second question, I suggest you first show that $\forall n\in\mathbb{Z}, f(n)=nf(1)$ . Then, you'll be able to show that $\forall r\in\mathbb{Q}, f(r)=rf(1)$ . As $\mathbb{Q}$ is a dense subset of $\mathbb{R}$ and $f$ is continuous, you'll be able to generalize the result to the real numbers.

Why don't you post text instead of images ? Images are annoying because one can't quote the question he is answering...

**ThePerfectHacker** · May 17th 2008, 06:04 PM

See this and this.

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