Day 07 in Mat122

Today:

• Hand back Homework 4.7: graded numbers 1 and 11 (out of 4 points total)
  • Why not check the roots with your calculator?
  • On #11, check for "convergence"
  • Even if you screw up, Newton's method may converge...
  • but it may converge to a different root!

• Hand in Homework 5.1

• Section 5.3: The Fundamental Theorem of Calculus, Part I
  • Well folks, here it is:

    It says that to integrate, all you have to do is think of an antiderivative F of the integrand f.

  • Let's derive/motivate the FTC using the linearization (again! wow, it's useful...)

  • Examples:
    • #12, p. 276
    • #40, p. 277
    • #49, p. 277

• Section 5.4: The Fundamental Theorem of Calculus, Part II
  • The news isn't earth-shaking: but it's certainly an interesting idea!

  • Now we arrive at the FTC, Part II:

  • Examples:
    • #1, p. 282
    • #8, p. 282
    • #16, p. 282
    • #20, p. 282
    • #23 p. 282
    • #46 p. 284