Day 27 in MAT229

Today:

• Announcements:
  • Exam 2: next week, 3/5: it will cover chapter 7, specifically.

  • HW4 is graded. In many cases a disaster. A few students came to see me. The ones who came to see me did well. Where were the rest of you?
    1. Please, please, please: find yourself some software, calculator, etc. that can check your answers. That first integral has value $\approx 1.70292$.

       If my answer is not $\approx 1.70292$, I'd better find out what the heck I'm doing wrong....

       Some of you neglected the long division. Alex, show the long division.

       You can do it without long division, however: Faith/Ramey.

       Some of you weren't sure what to do once you'd done the long division!

       Why leave an answer as $-3+\frac{3}{2}\ln(10)+tan^{-1}(3)$? That's as clear as mud. You'd better add $\approx 1.70292$.

    2. Algebra was a killer on 2. Never expand unless you have to. Bradley/David: solve for $y$

       Will, continue on. Elise finish.

    3. Caitlin start/Abby finish.

  • Spotlight on: Patrick!

  • I will post HW5 today, which will be due right after spring break.

• Today:
  • Half-time at the Motel $\infty$

    Countable infinities....

  • If we have time we'll also start the integral test, which is another way to show that an infinite series converges (by comparison with real-valued functions).

    Sect. 11.3: Integral test (pdf, pdf summary)

    • In particular I want to look at the so-called "harmonic series", and show why it is divergent.