Exam 3 Review Topics
Basics: L’Hopital Rule for undetermined forms: 0/0 form, 
form, 
form, 
form, 
form, 
form. Regular
partition of intervals, special Riemann sums: Left Point Sum, Right Point Sum.
Definition of anti-derivatives. Definition of definite integral. Definition of indefinite
integral. Geometric interpretation of definite integral in terms of area. Area
between two curves. Average value of a function, Mean Value Theorem. Simple
rules for definite integrals: Theorems 4.2 and 4.3. Fundamental Theorem of
Calculus I, Fundamental Theorem of Calculus II. Method of substitution. Graph
of antiderivative for function. Differential equations, solution to
differential equation, solution to differential equation with initial condition,
Parameterized curves, parameterized lines, parameterized circles and ellipse, tangent
lines to parameterized curves.
Techniques: L’Hospital Rules, using logarithm to transform and undetermined
forms. Hand calculation for left point sum, right point sum. Calculator computation
of left point sum, right point sum. Find anti-derivatives for all elementary
functions: power functions, exponential
functions, logarithmic functions, trigonometric functions, hyperbolic
trigonometric functions. Use method of substitution for finding indefinite
integrals. Derivative of area function in terms of definite integrals (i.e.
FTC-II). Properties of definitely integrals, linearity rule, additive of areas,
reversal of integration end points. Finding average value of a function. Antiderivatives
of elementary functions. Method of substitution. Verification of solution to
differential equation, Finding slope of parameterized
curves, finding concavity of parameterized curves. Calculator plot of
parameterized curves.
Elementary Functions: Properties of elementary functions: power functions, exponential
functions, logarithmic functions, trigonometric and inverse trigonometric
functions; derivatives of elementary functions, and antiderivatives of
elementary functions.
Calculator Skills: Approximating definite integrals by left, right point sum, sketch
graphs, sketch parametric curves, tracing intersection points and roots,
finding numerical limits.
Miscellaneous Techniques: Distance, area, volume formulas for elementary geometric objects:
rectangle, triangle, circle, ellipse, rectangular solid, cylinders.
Quadratic formula
for roots, factorization of a^2-b^2, a^3-b^3. 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 inverse trigonometric functions, and exponential and logarithmic
functions
Partial Review Problems: All homework, quiz, lecture
example problems, and sample exams. Repeat
the problems until you can do them without any help.
More review problems: p247: #24-38,53-55; p257:#8-11, 18,19, 27-29,46,47; p286: #3,4, 7, 8, 20,27-31; p296: #18,22,35,36,38; p305: #1-6,15-18,39-43,49-52; p323: #3-9,13,17-20; p330: #10-16, 43-49,68,71; p337: #1,2,7-10,16,21; p342: #4-14,17,18,23-26, 36-3839-42,48-53; p360: #3-8, 15-22, 23-28, 29-40, 41-46,53-56,57-64,69-70,71-76,79-81,97-100, 119-120,126.