14.3. Tables to Find Limits http://www.ck12.org
14.3 Tables to Find Limits
Here you will estimate limits using tables.
Calculators such as the TI-84 have a table view that allows you to make extremely educated guesses as to what the
limit of a function will be at a specific point, even if the function is not actually defined at that point.
How could you use a table to calculate the following limit?
limx→− 1 x^2 +x+^3 x 1 +^2
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/62306http://www.youtube.com/watch?v=l7Tcay720vw James Sousa: Determine a Limit Numerically
Guidance
If you were given the following information organized in a table, how would you fill in the center column?
TABLE14.1:
3.9 3.99 3.999 4.001 4.01 4.1
12.25 12.01 12.00001 11.99999 11.99 11.75It would be logical to see the symmetry and notice how the top row approaches the number 4 from the left and the
right. It would also be logical to notice how the bottom row approaches the number 12 from the left and the right.
This would lead you to the conclusion that the limit of the function represented by this table is 12 as the top row
approaches 4. It would not matter if the value at 4 was undefined or defined to be another number like 17, the pattern
tells you that the limit at 4 is 12.
Using tables to help evaluate limits requires this type of logic. To use a table on your calculator to evaluate a limit:
- Enter the function on they=screen
- Go to table set up and highlight “ask” for the independent variable
- Go to the table and enter values close to the number thatxapproaches