AP Calculus AB, unit: Limits and Continuity. Conceptual understanding and key rules for this unit, explained in plain language alongside the formula. Front: a concept or short problem cue. Back: the explanation, rule, or answer.
18 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a limit, informally?
- The value a function approaches as its input gets arbitrarily close to a point
- What is the notation for the limit of f(x) as x approaches c?
- lim(x to c) f(x)
- What does it mean for a limit to exist at a point?
- The left-hand and right-hand limits are equal at that point
- What is a one-sided limit?
- The value a function approaches as x approaches a point from only one direction
- What is the left-hand limit?
- The value a function approaches as x approaches a point from values less than it
- What is the right-hand limit?
- The value a function approaches as x approaches a point from values greater than it
- What happens if the left-hand and right-hand limits differ?
- The overall limit at that point does not exist
- What is a removable discontinuity?
- A point where a function is undefined or differs from its limit, but the limit still exists
- What is a jump discontinuity?
- A point where the left-hand and right-hand limits exist but are not equal
- What is an infinite discontinuity?
- A point where a function's value increases or decreases without bound
- What does it mean for a function to be continuous at a point?
- The function is defined there, the limit exists there, and they are equal
- What is the Intermediate Value Theorem?
- If a function is continuous on a closed interval, it takes every value between its endpoint values
- What is a limit at infinity?
- The value a function approaches as x grows without bound in the positive or negative direction
- What is a horizontal asymptote?
- A horizontal line a function's graph approaches as x approaches infinity or negative infinity
- What is a vertical asymptote?
- A vertical line where a function's value approaches infinity or negative infinity
FlashKeepers