MATH 1400 - Calculus I

1. Describe the one-sided or two-sided limits of a function numerically, graphically, or symbolically.
2. Demonstrate that a function is continuous at a given point or on a given interval.
3. Find all the numbers at which a function is continuous.
4. Compute a derivative using the definition.
5. Use a derivative to find the slope of the tangent line to the graph of a function at a point.
6. Find the equation of the tangent line and/or the normal line to the graph of a function at a point.
7. Find the average rate of change of a function over a given interval.
8. Find the instantaneous rate of change of a function at a point.
9. Find a derivative of a function by using the rules of differentiation.
10. Determine if a function is differentiable at a given point or on a given interval.
11. Use the concept of a derivative to determine if the graph of a function has a vertical or horizontal tangent line or cusp at a point.
12. Solve application problems involving differentiation, such as related rates and optimization problems.
13. Differentiate implicitly.
14. Use linear approximation to estimate the value of a function at a point.
15. Use a differential to approximate the change of the dependent variable given a change in the independent variable.
16. Use a differential to find the maximum error and the approximate relative error or percentage error in measurement of a calculated quantity.
17. Use Newton’s Method to approximate a specified quantity.
18. Find the critical numbers of a function.
19. Determine the extrema of a function on a closed or an open interval.
20. Show that a function satisfies the hypotheses of the Mean Value Theorem and find the value(s) that satisfy the theorem.
21. Use the first or second derivative tests appropriately to determine intervals on which the graph of a function is increasing, decreasing, or constant; intervals on which it is concave upward or concave downward; to find extrema; to find the points of inflection; and to sketch the graph of the function.
22. Use the first or second derivative test for solving optimization problems.
23. Find an antiderivative of a simple function.
24. Solve a simple differential equation.
25. Recognize limits that have an indeterminate form (quotient, product, difference, power) and apply L’Hospital’s Rule appropriately to evaluate them.
26. Find the Riemann sum for a function on an interval by choosing on each sub-interval the left-hand or right-hand endpoint or the midpoint.
27. Use a Riemann sum to find the exact value and approximate value of a definite interval.
28. Use rules of integration to find indefinite integrals and evaluate definite integrals.
29. Evaluate an integral by interpreting it in terms of areas.
30. Use the Fundamental Theorem of Calculus with theoretical and applied problems.
31. Use integration to find the average value of a function on a closed interval.
32. Find a number that satisfies the conclusion of the Mean Value Theorem for definite integrals.
33. Evaluate definite and indefinite integrals using basic u-du substitutions.
34. Use appropriate technology (graphing calculator, computer algebra system, etc.) where applicable in the above outcomes and interpret the results.

1. Techniques for finding limits
2. Techniques of differentiation
3. Implicit differentiation
4. Related rate problems
5. Linear approximations and differentials
6. Newton’s method
7. Extrema of functions
8. The Mean Value Theorem
9. Applications of the first and second derivative tests
10. Optimization problems
11. Velocity and acceleration problems and other application problems
12. Antiderivatives
13. L’Hospital’s Rule
14. Fundamental Theorem of Calculus
15. Interpreting and evaluating definite integrals
16. Basic u-du substitution

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2. The instructor will provide and schedule an exam date.
3. The student is to bring the Credit by Exam form to the scheduled exam.
4. The faculty member will notify the student and Records Office of the results.