please help with proofs of limits

[ocean tree]

Mk, so is this your proof or the teachers proof? I assume its the teachers as you seem to be confused.

To summarize we know that for delta 1 epsilon will hold true for f(x) and h(x) will hold true for delta 2. We know epsilon must be greater than 0, and so arbitrarily choose an epsilon greater than 0. Now if we do the scratch work for the 2 functions individually we are going to find a delta defined in terms of epsilon. Now because both functions are different naturally they will have different deltas when we choose to plug in an epsilon into both deltas. The deltas it will return gives us the max interval delta can be for the proof to hold true. Now we know that both functions are going to be within (L - E, L+E) as long as we are within their respective deltas. Now we have to choose a minimum delta because we can't have two deltas here. We know that if we take the minimum delta that the proof will hold true, because we know that delta 1 will hold true and so would delta 2. If we chose delta 2 as the minimum its obvious that its not a minimum, but the intuition behind it is that while if we chose delta 2 as our delta the problem is that while delta 2 would hold true h(x), it would not hold true for delta 1 of f(x) because we would then be outside of (L- E, L+ E) which we can't.

[gleaming prism]

yes it is my teacher's proof, thanks for responding

give me a sec to look at that

[ocean tree]

Mhmmm do take a look. So basically the premise of your question was why do we have a delta 1 and delta 2.

I basically explained the intuition behind why we choose a minimum delta which seemed to be your question.