15. LIMITS
15.1 Right-hand Limit
15.2. Left-hand Limit
15.3 Limit of a Function
15.4 Limit of a Polynomial Function
15.5 Limit of a Rational Function
15.6 Indeterminate Forms
15.7 Limit of a Radical Function
15.8 Limit of an Absolute Value Function
15.9 Limit of a Piece-wise Function
15.10 Limit of a Trigonometric Function
15.11 Limit of a Hyperbolic Function
15.12 Limit of an Exponential and Logarithmic Function
15.13 Limits at Infinity
Definition of a Limit
The limit of a function f(x) as the value of x approaches c is a real number L.
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In symbol, we have:
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Algebraically, limits can be evaluated from either left or right of c. The left-hand limit is found by replacing x with a real number less than but close to c. The right-hand limit is found by replacing x with a real number greater than but close to c. If the left-hand and right-hand limits are equal, then the limit of f(x) exists. Some functions will have a limit as x approaches c while others do not.
This section explores the algebraic approach to evaluating limits, infinite limits, and limits at infinity.
This section explores the algebraic approach to evaluating limits, infinite limits, and limits at infinity.
