**Final Exam Review Topic List**

**Limit: **Numerical method using
calculator; graphical method for e-d definition; L’Hopital
Rules for 0/0, ∞/∞ types; rational functions determined by their leading
degree terms; Squeeze Theorem. With applications in: finding horizontal,
vertical asymptotes; removable or nonremovable
discontinuities; finding derivatives by definition; finding definite integrals
by definition;

**Continuity:** Definition lim_{x}_{ → a} f(x) = f(a); Intermediate Value Theorem with application in finding
solutions to equations; Existence of absolute extrema
in closed and finite intervals.

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

**Integrals:** Definition of definite
integrals; meaning of definition integral in terms of signed area between the
curve and the x-axis. Special Riemann sums: left, right, midpoint, trapezoid,
and Simpson; calculation by hand, by calculator programs, by definition making
use of formulas: 1+2+…+n=n(n+1)/2,
1^2+2^2+3^2+…+n^2=(2n+1)n(n+1)/6. Under and over estimates by left, right,
midpoint, trapezoid sums in relationship to monotonicity
and concavity of functions. Average value of a function; Mean Value Theorem for
integrals: if f(x) is continuous
and c is in (a,b). Definition of indefinite
integral, antiderivative of functions. Elementary methods to find antiderivatives/indefinite
integrals: power rules, reversal of derivative formulas for elementary
functions, simplification/manipulation of integrants before integration, special
substitution: integral of f’(x)/f(x) type integrants, linearity rule of
integration, additive rule. Fundamental Theorems of Calculus: where F’(x) = f(x), and .

**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; approximating definite
integrals by left, right, mid, trapezoid, and Simpson rules.

**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.

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