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L IMITS AND L IMITS AT INFINITY Limit Review 1
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Limits can be calculated 3 ways Numerically Graphically Analytically (direct substitution) Properties of limits (pages 56-58)
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Graphically Determine the value of y as x approaches some number c
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Formal Definition of a Limit
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Analytic techniques Direct substitution Factoring- cancel common factors Rationalize- multiply by the conjugate
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1)Find 2) Find
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3) Find
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One sided limits left Right Limit existence
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4) Find
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5) Find
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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
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6) Find
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7) Find
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8) Find
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9) Find
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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
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10) Find
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11) Find
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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
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12) Find 13) Find
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14) Find and all asymptotes
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15) Findand all asymptotes
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H OME W ORK Limits Practice worksheet
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