All Flashcards
What is the formula for Average Rate of Change (AROC)?
What is the limit notation?
Define Average Rate of Change (AROC).
The slope of the secant line between two points on a function.
Define Instantaneous Rate of Change (IROC).
The slope of the tangent line at a single point on a function.
What is a limit?
The value a function approaches as the input (x-value) gets closer to a certain point.
What is a one-sided limit?
The limit as x approaches a value from either the left or the right.
What is a two-sided limit?
The limit as x approaches a value from both the left and the right. Both one-sided limits must be equal for it to exist.
Define jump discontinuity.
The function 'jumps' from one value to another.
Define removable discontinuity.
A 'hole' in the graph that can be 'filled' by redefining the function.
Define infinite discontinuity.
A vertical asymptote where the function approaches infinity or negative infinity.
What does it mean for a function to be continuous at a point?
f(a) is defined, the limit of f(x) as x approaches a exists, and the limit equals f(a).
Define vertical asymptote.
A vertical line x = a where the function approaches infinity or negative infinity as x approaches a.
What are the differences between removable and infinite discontinuities?
Removable: Limit exists, can be 'fixed'. Infinite: Vertical asymptote, limit DNE.
What are the differences between one-sided and two-sided limits?
One-sided: Limit from left or right. Two-sided: Limit from both sides, must be equal for the limit to exist.
What are the differences between average and instantaneous rate of change?
Average: Slope of secant line. Instantaneous: Slope of tangent line.