Chapter 1: Limits, Derivatives, Integrals, and Integrals - Vocabulary and Concepts

Contains concepts and vocabulary from Calculus: Concepts and Applications by Paul A. Foerster as taught by Colin Suehring at McFarland High School.

function

an expression, rule, or law that defines a relationship between one variable (independent variable) and another variable (dependent variable)

limit

the value that a function approaches as the input approaches some value

derivative

the slope of a line that lies tangent to the curve at the specific point or the limit of the average rate over the interval form c to x as x approaches c (instantaneous rate of change)

AROC

f(b)-f(a)÷(b-a)

IROC

slope of tangent line (derivative)

verbal definition of a limit

L is the limit of f(x) as x approaches c if and only if L is the one number you can keep f(x) arbitrarily close to just by keeping x close enough to c, but not equal to c

definite integral

the difference between the values of the integral at specified upper and lower limits of the independent variable (area under the curve)

the trapezoidal rule

Δx(½f(a) + f(x¹) + f(x²) + ... + f(xn-1) + ½f(b))

exact value of a definite integral

the limit of the trapezoidal rule sum Tn as n approaches infinity provided the limit exists

can be estimated numerically by taking trapezoidal sums with more and more increments and seeing whether the sums approach a particular number