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## PowerPoint Slideshow about ' 1.2 Finding Limits' - axel

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Presentation Transcript

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
- 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.

Numerical estimation

- Estimate the limit numerically by completing the table for

Answer

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

Graphical interpretation

- 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)

Answer

- 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 DNE

- Show limit DNE for
- Make a table or graph.

Answer

- Left L=-1 and right L=1
- -1≠1 so L=DNE
- Typical of step functions

Show DNE

- Show limit DNE for
- Make a table or graph.

Answer

- Both sides approach positive infinity which is not a #; therefore, L=DNE
- Typical of rational functions

Show DNE

- Show limit DNE for
- Make a table or graph.

Answer

- F(x) oscillates between -1 and 1 so L=DNE
- Typical of odd functions

Common behavior associated with DNE limits

- 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.

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