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## Limits and Limits at infinity

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**Limits and Limits at infinity**Limit Review 1**Limits can be calculated 3 ways**• Numerically • Graphically • Analytically (direct substitution) • Properties of limits (pages 56-58)**Graphically**• Determine the value of y as x approaches some number c**Analytic techniques**• Direct substitution • Factoring- cancel common factors • Rationalize- multiply by the conjugate**Find**2) Find**One sided limits**• left • Right • Limit existence**Infinite Limits**• Limit of f(x) increases or decreases without bound as x approaches some number c • Limit does not exist DNE • Vertical asymptotes occur when limits are infinite • Limit as x approaches 1**Limits at Infinity**• Identifies the behavior of the function as x tends to infinity • If , then L is a horizontal asymptote • Usually f(x) is rational • Limit as x approaches infinity**Limits at Infinity Shortcuts**• If the degree is higher in the denominator, then the limit is equal to zero • If the degree is higher in the numerator then the limit does not exist • If the degrees are the same, then the limit equals the ratio of the coefficients BOBO BOTN EATS DC**12) Find**13) Find**Home Work**Limits Practice worksheet