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Limits at Infinity definitions

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  • Limit
    The value a function approaches as its input gets arbitrarily close to a specific point or infinity.
  • Infinity
    A concept describing unbounded growth in either the positive or negative direction on the number line.
  • Rational Function
    An expression formed by dividing one polynomial by another, often analyzed for behavior at extreme values.
  • Numerator
    The top part of a fraction, whose degree is compared to the denominator when evaluating limits at infinity.
  • Denominator
    The bottom part of a fraction, whose degree influences whether a rational function's limit at infinity approaches zero.
  • Degree
    The highest exponent of x in a polynomial, crucial for determining the end behavior of rational functions.
  • Leading Coefficient
    The constant multiplying the term with the highest power of x in a polynomial, used in shortcut methods for limits.
  • End Behavior
    The trend of a function's output as the input becomes extremely large or small, often toward infinity.
  • Shortcut Method
    A quick technique for finding limits at infinity by comparing degrees and leading coefficients of numerator and denominator.
  • Oscillation
    A repeated up-and-down movement in a function's output, preventing the existence of a single limit at infinity.
  • Positive Infinity
    The direction on the x-axis representing values increasing without bound to the right.
  • Negative Infinity
    The direction on the x-axis representing values decreasing without bound to the left.
  • End Right Behavior
    The pattern a function follows as x increases toward positive infinity.
  • End Left Behavior
    The pattern a function follows as x decreases toward negative infinity.
  • Ratio of Leading Coefficients
    The value obtained by dividing the leading coefficient of the numerator by that of the denominator when degrees are equal.