Limits and Limits at infinity

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

Formal Definition of a Limit

Analytic techniques • Direct substitution • Factoring- cancel common factors • Rationalize- multiply by the conjugate

Find 2) Find

3) Find

One sided limits • left • Right • Limit existence

4) Find

5) Find

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

6) Find

7) Find

8) Find

9) Find

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

10) Find

11) Find

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

14) Find and all asymptotes

15) Find and all asymptotes

Home Work Limits Practice worksheet

Limits and Limits at infinity

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