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**MichaelJordan** $\displaystyle f$ is differentiable on $\displaystyle (a,b]$ and $\displaystyle f(x)/(x-a) \to 1$ as $\displaystyle x \to a+$, then $\displaystyle f$ is unifomliy continuous on$\displaystyle [a,b]$

Ok here is what I have so far. Let $\displaystyle f(x) = x$ and $\displaystyle g(x) = f(x)/(x-a) , g(a) = 0$. Now I need to show that $\displaystyle g$ is cont. at $\displaystyle a$ then I will have $\displaystyle g$ to be cont. on $\displaystyle [a,b]$ and I will be done right? So how in the world do I go about showing $\displaystyle g$ is cont. at $\displaystyle a$?