$$\lim_{x\to 0} 7e^{\dfrac x{(1-x)}}+1=8$$
I am trying to write epsilon-delta proof but I am stuck what i've got is:
$|e^{x/(1-x)}-1|< ε/7$
so my goal is to make it look like $|x|< δε$
I know that I can evaluate $|e^{x/(1-x)}-1|$ using remarkable limit and obtain: $$\lim_{x\to 0}\frac{(e^{x/(1-x)}-1) (x/(1-x))}{x/(1-x)}= 0,$$
but I have no idea how to proceed further
any hints?