# MAT 280: Exams

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.