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# 1.2 Finding Limits - PowerPoint PPT Presentation

1.2 Finding Limits. Limits described. Goal: To see how a function behaves near a point (such as a discontinuity) use 2 sets of x-values that approach from the left and the right of that point

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### 1.2 Finding Limits

• Goal: To see how a function behaves near a point (such as a discontinuity) use 2 sets of x-values that approach from the left and the right of that point

• Definition: if f(x) approaches a #, L, as x approaches c from either side, the limit of f(x) as x approaches c is L.

• Estimate the limit numerically by completing the table for

• Limit is L=1 because y-values on both sides of x=2 approach y=1

• Determine the limits at x=1, 2, 3, and 4 given the graph

• Remember limits occur at and when the y-values are the same as both sides of the c (x-values) approach c; otherwise L=DNE (does not exist)

• The limits for the various c values:

• C=1: L=1 (both sides approach y=1 despite point at y=2)

• C=2: L=DNE (left is at y=2 and right is at y=3)

• C=3: L=1 (both sides approach y=1)

• C=4: L=2 (both sides approach y=2)

• Show limit DNE for

• Make a table or graph.

• Left L=-1 and right L=1

• -1≠1 so L=DNE

• Typical of step functions

• Show limit DNE for

• Make a table or graph.

• Both sides approach positive infinity which is not a #; therefore, L=DNE

• Typical of rational functions

• Show limit DNE for

• Make a table or graph.

• F(x) oscillates between -1 and 1 so L=DNE

• Typical of odd functions

• F(x) approaches different # from right of c than approaches from left of c.

• F(x) increases or decreases without bound as x approaches c.

• F(x) oscillates between 2 fixed values as x approaches c.