We will have our first midterm exam on Thursday (Oct 13).  To prepare for the exam:

  • review the following WebWork exercises
    • Limits – Introduction: #5, 7, 8 (also solve the latter limit analytically!)
    • Limits – Analytic: #2, 3
    • Limits – One-Sided: #1-3
    • Limits – Continuity: #1-2
    • Derivative – Limit Definition: #2-3
    • Derivatives – Functions: #2-3
    • Derivatives – Power Rule: #2-9
    • Derivatives – Power Rule – Part 2: #1-4, 6-7
  • review Quiz #1 (solutions have been uploaded to Files)
  • review the following concepts:
    • the difference quotient, which gives the slope of a secant line:
Understand how this difference quotient relates the graphs below:
From https://openstax.org/books/calculus-volume-1/pages/3-1-defining-the-derivative
  • the definition of the derivative as the limit of difference quotients, which gives the slope of the tangent line to the graph y = f(x) at the point (a, f(a)):
From https://openstax.org/books/calculus-volume-1/pages/3-key-equations
  • finding the equation of the tangent line to y = f(x) at a point (x_1, f(x_1)) by using the point-slope equation of the line, with y_1 = f(x_1):
From https://openstax.org/books/calculus-volume-1/pages/1-2-basic-classes-of-functions

See Examples 3.1 – 3.3 in Sec 3.1 and Example 3.22 from Sec 3.3: