MAT-281 Objectives

MAT-281 Calculus I

Chapter P

  1. Use absolute value to define an interval.
  2. Plot data on a cartesian graph.
  3. Use regression capabilities of a graphing calculator.
  4. Find intercepts.
  5. Sketch graphs of equations (absolute value, linear).
  6. Find points of intersection.
  7. Find slope and y-intercept.
  8. Write the equation of a line using.
  9. Two points
  10. One point and the slope.
  11. Write equations of lines parallel to a given line.
  12. Write equations of lines perpendicular to a given line.
  13. Evaluate a function at a given value.
  14. Identify y as a function of x.
  15. Find composite functions.
  16. Find Real zeros of a function.
  17. Write functions from word problems.
  18. Solve a quadratic equation.
  19. Simplify algebraic expressions.

Chapter 1

  1. Use the definition of a limit to verify the validity of a limit. (Extra Credit!)
  2. Find the limit of an algebraic function.
  3. Find the limit of a trigonometric function.
  4. Find the limit of functions that begin as indeterminate.
  5. Find the limit of special trigonometric functions.
  6. Use the limit definition of velocity to solve falling object problems.
  7. Find one-sided limits of functions.
  8. Determine points of discontinuity.
  9. Identify discontinuities as removable or non-removable.
  10. Use interval notation to identify the domain of a function.
  11. Apply the Intermediate Value Theorem to the verification of a guaranteed value.
  12. Find vertical asymptotes of functions.
  13. Find one-sided infinite limits of functions.
  14. Apply limits to the solving of word problems.

Chapter 2

  1. Use the definition of the derivative to find f'(x) .
  2. Find the equation of a tangent line to a graph of f at a point.
  3. Find the equation of a line tangent to f and parallel to a given line.
  4. Use the Alternative Form of the derivative to find f'(c) .
  5. Find values of x where f(x) is differentiable.
  6. Find the derivative of a given function.
  7. Evaluate the derivative of a function.  
  8. Find the equation of a tangent line.
  9. Find the average rate of change.
  10. Solve falling body problems.
  11. Solve rate of change word problems.
  12. Differentiate algebraic functions.
  13. Differentiate trigonometric functions.
  14. Use power rule, product rule and quotient rule as needed.
  15. Find the second derivative.
  16. Find higher order derivatives.
  17. Solve velocity or acceleration problems.
  18. Apply the chain rule to find the derivative of composite algebraic functions.
  19. Apply the chain rule to find the derivative of composite trigonometric functions.
  20. Apply the chain rule to evaluate the derivative of composite functions.
  21. Apply the chain rule to solve word problems.
  22. Find dy/dx by implicit differentiation.
  23. Evaluate dy/dx at a given point.
  24. Find the second derivative in terms of x and y.
  25. Find the equations of tangent and normal lines to circles.
  26. Find the values of dx/dt or dy/dt.
  27. Solve related rate word problems for:
  28. Conic section forms,
  29. Right triangle forms,
  30. Angles of elevation,
  31. Linear vs angular speed.
  32. Cylinder forms
  33. Collected data types that require regression analysis.

Chapter 3

  1. Find critical numbers.
  2. Use a graphing calculator to:
  3. Graph functions
  4. Use zoom and trace features
  5. Use calc menu
  6. Use the table feature
  7. Use the regression capabilities
  8. Locate absolute extrema.
  9. Solve word problems related to extrema.
  10. Locate intervals where a function is increasing or decreasing.
  11. Determine the effect the relationship between f and g has on f' and g'.
  12. Find relative extrema.
  13. Find points of inflection.
  14. Sketch graphs.
  15. Solve word problems using relative extrema.
  16. Find limits as x goes to ¥.
  17. Sketch/analyze graphs that may have asymptotes.
  18. Sketch/analyze graphs of algebraic functions.
  19. Sketch/analyze graphs of trigonometric functions.
  20. Solve minimum/ maximum word problems of type:
  21. Sum or product of numbers,
  22. Area or volume.
  23. Find the differential dy
  24. Use differentials to approximate error.
  25. Use differentials to approximate roots or powers.
  26. Find Marginals.
  27. Solve maximum profit problems. 
  28. Solve minimum cost problems.
  29. Solve demand problems.

Chapter 4

  1. Evaluate indefinite integrals,
  2. Algebraic
  3. Trigonometric.
  4. Solve differential equations.
  5. Solve word problems,
  6. Growth,
  7. Vertical motion,
  8. Acceleration.
  9. Find sums.
  10. Use sigma notation to write sums.
  11. Use properties of sigma notation to evaluate sums.
  12. Find the limit of s(n) as n --> ¥.
  13. Use upper and lower sums to approximate the area of a region.
  14. Use the limit process to find the area of a region between a function and the x-axis.
  15. Set up a definite integral that yields a given area.
  16. Sketch the region indicated by a given integral.
  17. Use geometric formulas to calculate area.
  18. Given values of definite integrals find the values of related definite integrals.
  19. Evaluate the definite integral by the limit definition.
  20. Express a limit as a definite integral.
  21. Evaluate definite integrals of
  22. Algebraic functions,
  23. Trigonometric functions.
  24. Determine the area of regions bounded by graphs.
  25. Integrate to find F(X).
  26. Use the Second Fundamental Theorem of Calculus to find F'(x).
  27. Identify u and du for a given integral.
  28. Evaluate indefinite integrals a) algebraic, b) trigonometric, c) radicals
  29. Evaluate definite integrals.