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.
About this set
38 basic cards for AP Calculus. Set 1 of 8 in AP Calculus AB. It opens with "What is a limit, informally?" and "What is the notation for the limit of f(x) as x approaches c?". Study it alongside the other AP sets below.
38 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a limit, informally?
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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?
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lim(x to c) f(x)- What does it mean for a limit to exist at a point?
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The left-hand and right-hand limits are equal at that point- What is a one-sided limit?
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The value a function approaches as x approaches a point from only one direction- What is the left-hand limit?
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The value a function approaches as x approaches a point from values less than it- What is the right-hand limit?
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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?
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The overall limit at that point does not exist- What is a removable discontinuity?
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A point where a function is undefined or differs from its limit, but the limit still exists- What is a jump discontinuity?
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A point where the left-hand and right-hand limits exist but are not equal- What is an infinite discontinuity?
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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?
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The function is defined there, the limit exists there, and they are equal- What is the Intermediate Value Theorem?
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If a function is continuous on a closed interval, it takes every value between its endpoint values- What is a limit at infinity?
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The value a function approaches as x grows without bound in the positive or negative direction- What is a horizontal asymptote?
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A horizontal line a function's graph approaches as x approaches infinity or negative infinity- What is a vertical asymptote?
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A vertical line where a function's value approaches infinity or negative infinity
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