Hello everyone. Can someone show me how to do this proof please for my Real Analysis class? Proofs have always been a problem for me. I cant seem to get them to flow so any tips would be greatly appreciated.
Prove lim x->a f(x)/g(x) = L/M
Hello everyone. Can someone show me how to do this proof please for my Real Analysis class? Proofs have always been a problem for me. I cant seem to get them to flow so any tips would be greatly appreciated.
Prove lim x->a f(x)/g(x) = L/M
I've dragged this problem up again because I never really was able to finish it and I have a final next week and have a feeling something like this may be on it...
I need to do it using episilon delta definitions so it starts something like this
If 0$\displaystyle < \mid x - a \mid < \delta_1 \Rightarrow \mid f(x) - M \mid \leq \frac{\varepsilon}{2} = \varepsilon_1$
and $\displaystyle 0 < \mid x - a \mid < \delta_2 \Rightarrow \mid f(x) - N \mid \leq \frac{\varepsilon}{2} = \varepsilon_2$
Then by algebra... how Plato started it...
Now this is where I keep getting lost... I've spent many hours trying to get it where I can find $\displaystyle \varepsilon_1$ and $\displaystyle \varepsilon_2$. I always seem to end up with the g(x) somewhere and not able to get it so its all constants and substituted with $\displaystyle \varepsilon$ 's.