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We will have our second midterm exam on Thursday (Nov 10).  To prepare for the exam:

• review the following WebWork exercises
  • Derivatives – Product Rule: TBA
  • Derivatives – Quotient Rule: TBA
  • Derivatives – Rates of Change: #1, 3-5, 6(a)-(e), 7-9
  • Derivatives – Trigonometric: 1-7
• review Quiz #2 (solutions have been uploaded to Files)
• review the following concepts:
  • average rate of change/average velocity, as computed using the difference quotient (which also gives the slope of a secant line)
  • instantaneous rate of change, computed using the derivative
  • velocity and acceleration as first and second derivatives of position
  • derivatives of sin and cos (and how to find derivatives of the other trig functions using the quotient rule)
  • applying product and quotient rule, including to products and quotients involving trig functions

• 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):

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: