Day: October 11, 2022

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:

• 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)):

• 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):

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