I know how to do proofs of limits using the epsilon-delta definition of a limit. However I'm struggling with this particular problem:
Is this problem even possible to prove using algebraic manipulation to transform into (and arrive at some expression of delta in terms of epsilon)? Or does it require some other technique which I'm not aware of?
To prove this limit you need to show that . Working on the second inequality, we have
Now we need an upper bound for . Notice that by the triangle inequality.
If we restrict (say), then we would have
which gives
So continuing from we have
So finally, if we let and reverse each step, you will have your proof.