Topic: Real Analysis Continuity
Using epsilon-delta definition of continuous function, prove that f(x)=x^3+3x is continuous at x=-1

Topic: Real Analysis Continuity
Prove the converse of Proposition 1.2.8: Let S ⊂ R be nonempty and
bounded above, and let b0 be an upper bound of S. If
∀ ϵ > 0 ∃ x ∈ S : x > b0 − ϵ, (1)
then b0 = sup S