- #1
Whistlekins
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Homework Statement
We have [itex]f(x) = \frac{x^{2}+x-2}{x-1}+cos(x) , x\in\mathbb{R}\setminus \{1\}[/itex] and wish to prove that it is continuous on its domain.
Homework Equations
The delta-epsilon definition of the continuity of a function.
The Attempt at a Solution
I've managed to reduce [itex]|f(x) - f(x_0)| [/itex]to[itex] |x-x_0| + |cos(x) - cos(x_0)| < \delta + |cos(x) - cos(x_0)|[/itex]
I'm not too sure where to go from there or even if I'm on the right track. Any insight would be greatly appreciated.