GAIN AN ADVANTAGE
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- PDF: How to Make an A+ in Your First Calculus Course
Lesson Specific Problems
- Prove for a bounded function on [a,b] that if ϕ=Φ, then for every ϵ>0 there exists a δ>0 such that for all partitions P where ||P||<δ, then U(P)−L(P)<ϵ.
- Prove that every upper sum has a greatest lower bound.
- Prove that the set of all lower sums has a least upper bound.
- Prove that if f(x) is bounded on [a,b], then lim is the least upper bound of all lower sums.
- Prove that if f(x) is bounded on [a,b], then \lim_{||P\,||\to 0}\,U(P) is the greatest lower bound of all upper sums.
