Introduction to Limits definitions Flashcards
Introduction to Limits definitions
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Limit The y-value a function approaches as x gets arbitrarily close to a specific value from either side. One-sided Limit The value a function approaches as x nears a specific point from only one direction, either left or right. Left-sided Limit The value a function approaches as x gets close to a specific point from values less than that point. Right-sided Limit The value a function approaches as x gets close to a specific point from values greater than that point. Limit Notation A symbolic way to express the value a function approaches as x nears a specific point, often using 'lim' and arrows. Piecewise Function A function defined by different expressions over different intervals, often causing jumps or breaks in the graph. Jump Discontinuity A sudden change in a function's value at a point, causing the left and right limits to differ. Unbounded Behavior A situation where a function increases or decreases without bound as x approaches a specific value. Oscillation A function's repeated up-and-down movement near a point, preventing it from settling on a single value. Asymptote A line that a function's graph approaches but never touches, often causing unbounded behavior. Table of Values A numerical method for estimating limits by evaluating a function at points increasingly close to a target value. Graphical Method A visual approach to finding limits by observing the behavior of a function's graph near a specific x-value. DNE An abbreviation indicating that a limit does not exist at a particular point due to differing behaviors or unboundedness. Function Value The actual output of a function at a specific input, which may differ from the limit at that point. Approaching Value A value that x gets arbitrarily close to, but does not necessarily reach, when analyzing a function's limit.
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