1 Exam Review Topics
Basics: concept of limit, left and right limit; definition of continuity; removable and nonremovable discontinuity; Intermediate Value Theorem; concept of horizontal, vertical, slant asymptotes; definition of derivative; tangent line, secant line; concept of average and instantaneous slopes/velocities; Techniques: find limits by numerical and graphical means, find limits of undetermined types: /, 0/0; find limits by Squeeze Theorem; find limits by definition; find limits by power rules, linearity rule; find horizontal, vertical, slant asymptotes (using long division); find roots of polynomials through factorization; application of Intermediate Value Theorem to determine the existence of roots of functions and the conceptual algorithm of bisection; simplify expressions involving exponential and logarithmic functions and find exact (not calculator assisted numerical) solutions to equations with elementary functions; find equations of tangent lines and sketch tangent lines; transform and sketch graphically for f(x) + b, f(x+b), af(x), f(ax) if f(x) is given; sketch function if f(x) its derivative f'(x) is given; sketch the derivative function f'(x) if the function f(x) is given; hand sketch lines, parabola, cubic functions, trigonometric functions, trigonometric functions with varying amplitudes, exponential functions, and logarithmic functions 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 func...