Exam 1 Review Topics

 

Basics: concept of limit, left and right limit; definition of continuity; tangent line, secant line; concept of average and instantaneous slopes/velocities; definition of derivative, rate of change, slope of curve, second and higher order derivatives, acceleration

 

Techniques: find limits by numerical and graphical means using graphical calculator; find limits of undetermined types: ∞/∞, 0/0; find limits of rational functions, linearity rule; find roots of polynomials through factorization; finding derivative by definition; derivatives of elementary functions including polynomials, exponential functions, and trigonometric functions; differentiation rules: linearity rule, product rule, quotient rule, chain rule, and implicit differentiation; find equations of tangent lines and sketch tangent lines; sketch the derivative function f (x) if the function f(x) is given and vice versa; sketch the second derivative function f(x) if f(x) or f(x) is given and vice versa; find intervals of increasing and decreasing; find intervals of concave up and concave down; hand sketch lines, parabola, cubic functions, trigonometric functions with different periods, exponential functions, trigonometric functions with varying amplitudes

 

Elementary Functions: basic forms and shapes of polynomials: linear function, parabola, cubic polynomials; definitions of trigonometric functions; exponential functions, log functions and their algebraic properties and rules; basic identities of trigonometric functions including the summation angle and double angle formulas; special values of trigonometric functions; derivatives of these 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; simplifying techniques: multiply and divide a same quantity, add and subtract a same quantity to maintain and transform quantities

 

Partial Review Problems: All homework, quizzes, lecture example problems, and sample exams