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 $\phi=\Phi$, then for every $\epsilon\gt 0$ there exists a $\delta\gt 0$ such that for all partitions $P$ where $||P||\lt\delta$, then $U(P)-L(P)\lt\epsilon$.
- 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 \[\lim_{||P\,||\to 0}\,L(P)\] 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.
