12-01: Rates of Change

AROC

AROC

________- average rate of change: rate of change over an interval, between 2 points → corresponds to the slope of the secant line.

IROC

________- instantaneous rate of change: rate of change at an instance, at a single point → corresponds to the slope of the tangent line.

hand limits

Left ________: use values that are less than or to the left side of the value being approached.

Jump discontinuity

________: One sided limits exist but are not equal.

Removable discontinuity

________: Hole (when factor cancels in equation)

Dependent variables

________: depend on the independent variables, are an outcome.

Rate of change

the change in one quantity (dependent variable) with respect to another quantity (independent variable)

Slope = ∆y/∆x = (y2

y1)/(x2-x1)

Independent variables

are picked and can be controlled, e.g

Dependent variables

depend on the independent variables, are an outcome

Proceeding and Following method

use the point (data) before and after tangent point to find the IROC of the tangent point

Slope = ∆y/∆x = (y2

y1)/(x2-x1)

As this happens, the slope of the secant line approaches its limiting value

the slope of the tangent line

Left hand limits

use values that are less than or to the left side of the value being approached

Right hand limits

use values that are greater than or to the right side of the right side of the value being approached

Continuous function

a function that is continuous at x for all values of xER

Piecewise function

a function made up of 2 or more functions, each corresponding to a specific interval within the entire domain (each graph has its own domain)

Removable discontinuity

Hole (when factor cancels in equation)

Jump discontinuity

One sided limits exist but are not equal

Infinitely discontinuity

one sided limit is infinite so limit doesnt approach a particular finite value and limit does not exist