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Topics for Calculus I Exam

posted Dec 20, 2017, 7:57 AM by Matthew Grenfell
  • Limit rules allowing limit computations.
  • Limit Computations. 
  • Understanding an indeterminate form when regarding limits.
  • Being able to correctly use L’Hôpital’s rule in calculating limits. 
  • Understanding continuity and it implications.
  • Differentiating using the differentiation rules for functions involving algebraic, trigonometric, exponential and logarithmic functions.
  • Understanding how to differentiate implicitly.
  • Being able to compute a tangent line to a differentiable function. 
  • Optimization (maximum-minimum applied questions).
  • Computing areas between curves and bounded by curves.
  • Understanding the use of f’ and f’’ in determining qualities of f. 
  • Understanding what critical numbers of a function are. 
  • Understanding how to solve applied rate of change questions.
  • Understanding the nature of a definite integral, even with a parameter involved.
  • Definite and indefinite integration, including the use of u-substitution.
  • Understanding volumes of revolution 
  • Understanding the interplay between distance, velocity and acceleration of an object.
  • Being able to compute a tangent line to a differentiable function
  • Understanding the difference between displacement and total distance traveled given a velocity function
  • Determining analytically graphical aspects of the graph of a function.
  • Recognizing and using for computation, the limit definition of a derivative to find the derivative of a function.
  • Being able to find vertical and horizontal asymptotes with justification of their answers.
  • Optimization questions.
  • Understanding the Extreme Value Theorem.
  • Average velocity given the position function and instantaneous velocities at a point in time when a given position is attained.
  • Understanding Riemann sums.
  • Working with models of growth and decay.
  • More differentiation using the differentiation rules for functions involving algebraic, trigonometric, inverse trigonometric, exponential and logarithmic functions.
  • More questions using u-substitution for indefinite and definite integration. 
  • Understanding the Fundamental Theorem of Calculus, both parts and using them.
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