Limits at Infinity definitions Flashcards
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.
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