Calculus I

Calculate limits using graphical, algebraic and numerical methods and the Squeeze Theorem.

Determine continuity of a function at points, identify various types of discontinuities and identify intervals of continuity for functions.

Calculate derivatives from the definition and using differentiation rules and implicit differentiation.

Use differentiation to identify tangent lines, to solve geometric problems and to solve problems involving rates of change.

Solve optimization and related-rates problems by analytic methods.

Graph a function, showing all relevant information such as relative extrema, inflection points, and asymptotes, with analytic methods and without the aid of graphing technology.

Approximate roots of equations by using the bisection method and Newton¿s method.

Calculate integrals by using the Fundamental Theorem of Calculus, u-substitution, and observations about symmetry of graphs.

Use integration to find the area under a curve, to solve problems involving net change, and to solve other geometric problems.

State and apply named theorems of calculus (the Intermediate Value Theorem, the Mean Value Theorem, and the Fundamental Theorem of Calculus).

Identify whether a derivative or an integral (or neither) is more appropriate for use in a given problem.

Communicate their knowledge of the basic principles of Calculus I, both orally (e.g. class discussions) and in writing (e.g. written assessments).