**Final Exam Review Topic List**

**Limit: **Finding limit using graphs
(for piecewise continuous functions); finding limit numerically using
calculator; L’Hopital Rules for 0/0, ∞/∞
types; rational functions determined by their leading degree terms; finding
derivatives by definition.

**
Derivatives:**
Definition, f’(x) = lim

**Integrals:** Definition of definite
integrals; meaning of definite integral in terms of signed area between the
curve and the x-axis. Special Riemann sums: left endpoint, right endpoint rules/formulas
for numerical approximation; calculation by hand. Average value of a function and the Mean
Value Theorem for integrals: if f(x) is continuous
and c is in (a,b). Definition of antiderivative/indefinite integral. Elementary
methods to find antiderivatives/indefinite integrals:
power rules, reversal of derivative formulas for elementary functions,
simplification/manipulation of integrants before integration, method of
substitution, linearity rule of integration, additive rule. Fundamental
Theorems of Calculus: where F’(x) = f(x), and . Find specific values of the antiderivative
of a function which is given graphically.

**Elementary Functions:** basic forms and shapes of
polynomials: linear function, parabola, cubic polynomials, definitions of
trigonometric functions, exponential functions, and logarithmic functions,
basic identities of trigonometric functions including double angle and half
angle formulas, basic rules, identities, and limiting properties as x → ∞
for exponential and logarithmic functions, special values of trigonometric
functions and exponential and logarithmic functions; Derivatives of power
functions, exponential functions, logarithmic functions, trigonometric
functions; antiderivatives of power functions,
exponential functions, trigonometric functions.

**Calculator Skills:** Sketch graphs, tracing
intersection points and roots, finding numerical limits.

**Miscellaneous Techniques: **quadratic formula for roots,
factorization of a^2-b^2, a^3-b^3, long division, multiply and divide to
maintain and transform quantities. Distance and speed.
Area, volume formulas for elementary geometric objects: rectangle, triangle,
circle, ellipse, rectangular solid, cylinders.

**Critical Skills:** Proficiency in college
algebra; proper use of parentheses.

**Partial Review Problems**: All homework, quizzes, lecture example problems,
sample hour exams, and sample final exams.

**Study Tips:** __Repeat homework/quiz/test problems until
you can do them without any help, not by memorization but by reasoning. Before
you can do this don’t try any sample final exam. __