MATH 255A, Review for the Final Exam

Course website: http://www.csun.edu/~panferov/math255a/

New material (since Test 3)

  1. Antiderivatives and the indefinite integral (7.1).
  2. Integration by substitution (7.2) Integration by substitution for definite integrals (7.4).
  3. Area and the definite integral. Riemann's sums (7.3).
  4. The fundamental theorem of calculus (7.4).

The final exam will be cumulative, but it will put a certain emphasis to the new material (at least three problems in the exam will be on integration).

Some of the important topics/types of problems

  1. Functions, domains, asymptotes. (Chapters 1 and 2). Graphs of the elementary functions (page 127) (1.R: 33, 39, 40, 49, 53, 2.R: 2, 71, 73)
  2. Continuity, especially for piecewise defined functions (Example 2 in 3.2, problems 3.2: 21-25 (odd), 3.R: 31).
  3. Limits, including left and right limits. Limits at infinity and their relation to asymptotes (3.R: 21; 26, 27, 28 (find the left and right limits))
  4. Derivatives. Rules of differentiation, particularly the chain rule (4.R)
  5. Antiderivatives, integration by substitution (7.2: 23, 31 7.R: 21, 49)
  6. The derivative using the formal definition (3.R)
  7. Equation of a tangent (3.R)
  8. Area between the graph and the x-axis (7.R: 59, 61, 63)
  9. Estimating the integral by using Riemann's sum (sum of the rectangles) (7.3: 9, 11)
  10. Maxima/minima on bounded intervals (6.R)
  11. Word problems on maxima/minima (6.R)
  12. Word problems involving exponential/logarithmic or trigonometric functions 2.R: 90, 91, 97
  13. Sketching graphs of functions using the techniques of Chapter 5 (5.R)

Formulas to memorize

Everything that was mentioned for Tests 1, 2 and 3, plus the antiderivatives of the following functions, xn, 1/x, emx, sin(x), cos(x).