Studied by 30 people
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
