Learning Outcomes

Assessment

1. Determine the existence of, estimate numerically and graphically, and find analytically the limits of functions.

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2. Determine the continuity of functions at a point or on intervals.

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3. Recognize and determine infinite limits and limits at infinity.

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4. Determine the derivative of a function using the limit definition and derivative theorems (sum/difference rules, power rule, chain rule, product rule, quotient rule, derivatives of logarithms and exponentials) and understand the correlation of the derivative to finding tangent lines to a graph, finding the slope of a graph at a point, and finding the rate of change of a dependent variable with respect to an independent variable.

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5. Solve applied problems involving marginal cost and/or marginal revenue.

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6. Demonstrate the ability to determine higher order derivatives of a function.

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7. Determine absolute extrema on a closed interval for continuous functions and to use the first and second derivates to analyze and sketch the graph of a function, including determining intervals on which the graph is increasing, decreasing, constant, concave up, concave down, and any relative extrema or inflection points.

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8. Solve applied optimization problems.

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9. Demonstrate the ability to determine indefinite and definite integrals, use the Fundamental theorems of Calculus, and integrate by substitution.

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10. Use integrals to solve basic initial condition problems such as finding the revenue function given a marginal revenue function.

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11. Use definite integrals in applications such as determining the area of an enclosed region, finding the average value of a function, and business applications.

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12. Solve business applications using differential and integral calculus.

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13. Demonstrate the application of the following classes of functions: polynomial, rational, algebraic, exponential and logarithmic.

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