Outcomes

At the completion of this course the student will:

  • Calculate or estimate limits of given functions, graphs, tables including L'Hopital's Ruleli>
  • Determine   whether a function given by a graph or formula is continuous or differentiable at any given point.
  • Distinguish between average and instantaneous rate of change, and interpret the definition of the derivative graphically.
  • Calculate derivatives of polynomial, rational, common transcendental functions, combinations of these functions, and implicitly defined functions.
  • Apply the ideas and techniques of derivatives to related rate problems.
  • Finding extreme values of modeling functions given by formulas or graphs
  • Estimate a slope, a rate of change and the reasonableness of a result.
  • Interpret solutions to applied problems, attaching the appropriate units to an answer.
  • Calculate the Riemann sum for a given function, partition and collection of evaluation points
  • Describe a definite integral as the limit of a Riemann sum,  the area under a curve,  the distance traveled by a moving object,  and a total accumulation.
  • Determine the appropriate units for a definite integral.
  • Describe the meaning of the antiderivative of a function.
  • Determine the antiderivatives of polynomial, trigonometric, exponential and logarithmic functions.
  • Determine the values of definite integrals using antiderivatives and areas.
  • Approximate the numerical values of definite integrals.
  • State and paraphrase the Fundamental Theorem of Calculus.
  • Apply the ideas of definite integrals to solve problems area and volumes
  • Distinguish assumptions and conclusions in mathematical statements.
  • Become an intermediate to expert user of the graphing calculator (TI-89)