Business Calculus MATH 1325

David Katz, instructor

Section by Section List of Test Topics for Exam #4 (Chapter 7) from Calculus With Applications by Lial et als. (8th edition)

The exam will consist of 20 multiple-choice questions from this list of topics from your homework sections.

  1. In general, know that a marginal function usually means a derivative function
  2. In general, know basic business formulas: P = R – C and R = xp
  3. (7.1) Know the proper symbols for antiderivatives (indefinite integrals); don’t forget the arbitrary constant!
  4. (7.1) Know the rules of integration: Power Rule, Constant Rule, Sum/Difference Rule, Exponential Rule, Logarithm Rule
  5. (7.1) Find an antiderivative using the rules of integration
  6. (7.2) Know when to use u-substitution to find an antiderivative (p.399)
  7. (7.2) Use u-substitution to find an antiderivative
  8. (7.2) Use information from an applied problem to solve for the arbitrary constant in an antiderivative
  9. (7.3) Compute approximate area under the curve using the sum of areas of rectangles (left endpoint or right endpoint)
  10. (7.3) Know when to use a geometry formula for area of a circle or triangle to compute the exact area under the curve
  11. (7.4) Know the Fundamental Theorem of Calculus and the relationship between definite integrals and antiderivatives
  12. (7.4) Compute a definite integral to find the exact area between a curve and the x-axis
  13. (7.4) Know that finding a total function usually means computing a definite integral
  14. (7.4) Know that definite integral can be positive, negative, or zero in value
  15. (7.4) Locate the x-intercepts of the graph of a basic function to know when area under the curve is negative or positive
  16. (7.4) Know that total area under the curve is the positive sum of all subregions when the graph is above or below the x-axis
  17. (7.4) Compute total area using the absolute value of a definite integral when necessary to guarantee area is always positive
  18. (8.2) Compute volume of a solid by the revolution along the x­-axis
  19. (8.2) Compute average value of a function over an interval of x
  20. (10.1) Solve a differential equation by integrating both sides of the equation
  21. (10.1) Solve a differential equation by separating variables first and then integrating
  22. (10.1) Use an initial condition in an applied problem to find a particular solution (i.e., solve for the arbitrary constant after integrating)

 

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