Exam 3 Review Topics

 

Basics: †††††LíHopital 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: LíHospital 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.