Proving with Delta Epsilon: A Beginner's Guide

[conorsmom]

Hi there, I'm having trouble understanding how to prove things using the $$\delta$$ $$\epsilon$$ definition. I have read a few other threads and sites, but I can't seem to put it together. For example, I came across this problem, if given lim_x-->af(x) = L, how would I prove (using delta-epsilon and without assuming that the limit of a sum of two functions is the sum of their individual limits) that the lim_x-->a[x+f(x)]=a+L ?

Thanks for the help!

 

[elibj123]

(using delta-epsilon and without assuming that the limit of a sum of two functions is the sum of their individual limits)

You can always use the same proof sketch of limit arithmetics, only specifically applied to your case ;)

 

[radou]

Hint: use ε/2.