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### Topics for Calculus I Exam

posted Dec 20, 2017, 7:57 AM by Matthew Grenfell   [ updated May 14, 2019, 4:23 AM ]
 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 functionUnderstanding the difference between displacement and total distance traveled given a velocity functionDetermining 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.