- 2 | Limits and Their Properties
- 3 | Differentiation
- 4 | Applications of Differentiation
- 5 | Integration
- 7 | Applications of Integration
- MAT 280: Homework
- MAT 280: Sandbox
- MAT 280: Challenge
- MAT 280: Quizzes
- Differentitation Rules Reference Page
- Integration Rules Reference Page

Exam outlines serve as a guide as to what you can expect to see on exams.

- In terms of definitions and theorems, I will only ask you to state the Fundamental Theorem of Calculus and the limit definition of the derivative.
- There will be a graph and you’ll be asked questions related to the graph (i.e. limits, derivatives, continuity, intervals of increase/decrease/constant, absolute max/min, relative max/min, definite integrals, areas of bounded regions, etc…)
- Find the limit of a function using general properties of limits and basic rules of limits.
- Determine if \(f(x)\) is continuous at \(c\).
- Find the derivative of a function using general properties of derivatives and basic rules of differentiation.
- Find the antiderivative of a function using general properties of antiderivatives and basic rules of integration.
- Find the absolute extrema of \(f(x)\) on a closed interval \([a,b]\).
- Find the relative extrema.
- Find the average value of a function on \([a,b]\)
- Find a \(c\) that satisfies the Mean Value Theorem for Integrals
- Sketch the graph of a function using calculus techniques.
- Determine the intervals on which \(f(x)\) is concave up or concave down.
- Find an equation of the tangent line.
- Find inflection points.
- Find horizontal and vertical asymptotes.

- Exam 3 Solutions
- State the definition of an antiderivative
- State the Fundamental Theorem of Calculus
- State the definition of average value of a function
- There will be a graph and you’ll be asked questions related to the graph (i.e. limits, derivatives, continuity, intervals of increase/decrease/constant, absolute max/min, relative max/min, definite integrals, areas of bounded regions, etc…)
- Find the indefinite integral of a function (There are at least a couple of these)
- Evaluate a definite integral (There are at least a couple of these, one of which will involve an absolute value).
- Find the average value of a function on an interval
- Take the derivate of a function defined as an integral.
- Find an indefinite integral using u-sub. One of these will be such that the old variable will not completely cancel after making the substitution.
- Sketch and find the area of a region bounded by the graphs of some equations (There will be at least two of these).

- Exam 2 Solutions
- State the Extreme Value Theorem
- State the Rolle’s Theorem
- State the Mean Value Theorem
- There will be a graph and you’ll be asked questions related to the graph (i.e. limits, derivatives, continuity, intervals of increase/decrease/constant, absolute max/min, relative max/min, etc…)
- Find the absolute extrema of \(f(x)\) on a closed interval \([a,b]\).
- Find the relative extrema.
- Determine the intervals on which \(f(x)\) is increasing, decreasing, or constant.
- Determine the intervals on which \(f(x)\) is concave up or concave down.
- Find inflection points.
- Find horizontal and vertical asymptotes.
- Sketch the graph of a function (2 problems) one of which will be a rational function.

- Exam 1 Solutions
- I recommend answering the following three items exactly as they appear in the notes.
- State the limit definition of the derivative.
- State the Intermediate Value Theorem.
- State the Squeeze Theorem.
- There will be a graph and you’ll be asked questions related to the graph (i.e. limits, derivatives, continuity, etc…)
- Evaluate limits with indeterminate form 0/0.
- Evaluate limits for a piecewise function.
- Given a piecewise function with an unknown constant, find a choice of that constant so that the function is continuous at a particular \(x\) value or on \((-\infty, \infty)\).
- Evaluate limits: from the left, right, both-sides.
- Find an equation of the tangent line.
- Find the derivative of a function using basic rules and general properties of differentiation. This includes any of the derivative rules that can be found on the Derivative Rules Reference Page.
- Find the derivative of a function using the limit definition of the derivative.
- Find higher order derivatives.
- Find the derivative using implicit differentiation.
- Find an equation of the tangent line to the graph of an equation that is relates y as a function of x implicitly.