Exam 1 Review Topics


Basics: concept of limit, left and right limit; definition of continuity; removable and non-removable discontinuity; concept of horizontal, vertical, oblique asymptotes; definition of derivative; tangent line, secant line; concept of average and instantaneous slopes/velocities; concept and definition of derivative, rate of change, slope of curve, second and higher order derivatives, acceleration


Techniques: find limits by numerical and graphical means; find limits of undetermined types: ∞/∞, 0/0; find limits by Squeeze Theorem; find limits by power rules, linearity rule; find horizontal, vertical, oblique asymptotes (using long division); find roots of polynomials through factorization; finding derivative by definition; derivatives of elementary functions including polynomials, 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; hand sketch lines, parabola, cubic functions, trigonometric functions, 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; basic identities of trigonometric functions including summation angle, double angle, half 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