Investigate uniform continuity of the following functions: $$a) \ f(x)=\frac{1}{x} \\ b) \ f(x)=\cos \frac{1}{x}$$ How to deal with such questions, i have little knowledge about that topic thus i would appreciate detailed explanaitions.
EDIT: Will something change if i will define $f:(0,1)\rightarrow \mathbb{R}$?
Function b is not uniform continious: Example $x_{n}=1/{(2\pi*n)}->0$ $y_{n}=2/{(\pi*n)}->0$ $f(x_{n})->1$ but $f(y_{n})->0$. b(x) is not continious, and then is not also uniform continous. a) is not uniform continious see page 2: http://www.math.ku.edu/~lerner/m500f09/Uniform%20continuity.pdf