1.2 Finding Limits

1 / 13

# 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

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

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

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### 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
• 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
• 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)
• 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.
• 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.