- State and explain the informal definition of limit.
- Estimate limits graphically and numerically.
- State and explain, with examples, the ways limits may fail to exist.
- Estimate and evaluate one-sided limits.
- Use one-sided limits to justify that a limit does not exist.
- Determine one-sided and two-sided infinite limits.
- Find and sketch the vertical asymptotes of the graph of a function.

- Use limit laws to evaluate limits.
- Use substitution to evaluate limits.
- Use algebraic techniques to resolve 0/0 indeterminate forms.
- Use the squeeze theorem to evaluate limits.
- Use trigonometric techniques to resolve 0/0 indeterminate forms.

- Use the definition of continuity to determine if a function is continuous at a point.
- Use the properties of continuity to determine if a function is continuous at a point or on an interval.
- Classify discontinuities.
- Apply the Intermediate Value Theorem.

- Use the formal definition of limit to prove certain limits.
- Find a delta corresponding to a particular epsilon by using analytical, numerical, or graphical techniques.

- State, explain, and illustrate the limit definition of derivative.
- Use the limit definition of derivative to evaluate a derivative.
- Interpret the derivative as the slope of a tangent line.
- Find equations of tangent lines.
- Determine when a derivative does not exist.
- Graph the derivative function from the graph of a given function.

- Evaluate derivatives (and higher-order derivatives) using basic differentiation rules.

- Calculate an average rate of change (i.e., slope of a secant line).
- Interpret the derivative as an instantaneous rate of change.
- Solve problems involving motion along a line.
- Solve various application problems involving rates of change.

- Evaluate derivatives of trigonometric functions.

- Identify compositions of functions, and write a function as a composition of two functions.
- Use the chain rule to differentiate compositions of functions.

- Use implicit differentiation to find the derivative of an implicitly-defined function.
- Find equations of the lines tangent and normal to the graph of an implicitly-defined function.

- Compute the derivative of an inverse function.
- Evaluate derivatives involving the inverse trigonometric functions.

- Compute the derivative of an exponential function of any base.
- Compute the derivative of a logarithmic function of any base.
- Use logarithmic differentiation.

- Use implicit differentiation to relate rates.
- Solve application problems involving related rates.

- Determine the linearization of a function at a point.
- Use the linearization at a point to approximate function values near the point.
- Compute differentials.

- Find the critical numbers of a function.
- Determine whether an extreme value is absolute or relative.
- Find the absolute extreme values of a continuous function on a closed, bounded interval.

- State, explain, and apply Rolle's Theorem.
- State, explain, and apply the Mean Value Theorem.

- Use the first derivative to find intervals on which a function is increasing/decreasing.
- Use the first derivative test to locate relative extrema.
- Use the second derivative to find intervals on which the graph of a function is concave up/down.
- Find the points of inflection of the graph of a function.
- Apply the second derivative test to classify relative extrema.

- Evaluate limits at infinity.
- Find the horizontal asymptotes of the graph of a function.

- Use calculus techniques to solve application problems involving optimization.

- Identify indeterminate forms.
- Apply L'Hopital's rule to resolve indeterminate forms.
- Use algebraic techniques to rewrite limits so that L'Hopital's rule applies.

- Use Newton's method to approximate the zeros of a function.
- Use tangent lines to illustrate Newton's method.

- Use basic integration rules to evaluate indefinite integrals.
- Solve initial value problems.

- Use rectangles to approximate the area of a bounded region under the graph of a function.
- Use upper and lower sums to approximate area.
- Compute a Riemann sum for a function on an interval.

- Define and interpret the definite integral of a function on an interval.
- Use Riemann sums to approximate definite integrals.
- Use properties of the definite integral to simplify and evaluate integrals.
- Use area to evaluate definite integrals.
- Use the definite integral to define the average value of a function.

- Use the Fundamental Theorem of Calculus to evaluate definite integrals.
- Use and evaluate definite integrals in applications involving area and average value.
- Interpret an integral with variable bounds as an accumulation function.
- Use the Fundamental Theorem of Calculus to differentiate functions defined by integrals.

- Use substitution to evaluate indefinite integrals.
- Use substitution to evaluate definite integrals.

- Evaluate integrals involving exponential functions.
- Evaluate integrals that result in logarithmic functions.
- Evaluate integrals that result in inverse trigonometric functions.

*Last updated December 6, 2021*