Math 1A (Calculus): Ch. 1 & 2 Notes

mathematical models, essential functions, linear models, polynomials, power functions, rational functions, algebraic functions, trigonometric functions

new functions from old functions, exponential functions, translating graphs, stretching graphs, squeezing graphs, reflecting graphs, combination of functions, composition of functions, composition of 3 or more functions, Euler's number, natural exponential function

inverse functions, inverse logarithms, tangent problems, velocity problems, one-to-one functions, domain of inverse functions, range of inverse functions, logarithms, decay, inverse trigonometric functions, slope of a tangent line, slope of a secant line, average velocity, instantaneous velocity, li...

limit laws, direct substitution property, limit theorems, one-sided limits, squeeze theorem

precise definition of a limit, delta, epsilon, infinite limits

continuity, definition of a continuous function, theorems of continuous functions, intermediate value theorem, bisection method to approximate the root

limits at infinity, horizontal asymptotes, definition of a horizontal asymptote, squeeze theorem, limit laws, infinite limits at infinity, computing with infinity, tangent and velocity problems, derivatives, rates of change, instantaneous rate of change, the derivative as a function