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Introduction to Limits definitions

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  • Limit
    The y-value a function approaches as x gets arbitrarily close to a specific value, regardless of the function's value at that point.
  • One-sided Limit
    The y-value a function approaches as x nears a specific value from only one direction, either left or right.
  • Left-sided Limit
    The y-value a function approaches as x gets close to a specific value from values less than that point.
  • Right-sided Limit
    The y-value a function approaches as x gets close to a specific value 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 arrows and subscripts.
  • Piecewise Function
    A function defined by different expressions over different intervals, often causing jumps or discontinuities.
  • Discontinuity
    A point where a function is not continuous, often resulting in jumps, holes, or breaks in the graph.
  • Unbounded Behavior
    A situation where a function increases or decreases without bound as x approaches a specific value, often heading to infinity.
  • Oscillation
    A behavior where a function rapidly alternates between values as x approaches a point, preventing the limit from existing.
  • Asymptote
    A line that a function approaches but never touches, often associated with unbounded behavior in limits.
  • Table of Values
    A numerical method for estimating limits by evaluating the function at points increasingly close to the target x-value.
  • Graphical Method
    A visual approach to finding limits by observing the trend of a function's graph near a specific x-value.
  • DNE
    An abbreviation indicating that a limit does not exist due to differing one-sided limits, unbounded behavior, or oscillation.
  • Function Value
    The actual output of a function at a specific input, which may differ from the value approached by the limit.
  • Infinity
    A concept describing unbounded growth or decrease, not a real number, often appearing in limits with unbounded behavior.