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1.2 Finding Limits

1.2 Finding Limits. Numerically and Graphically. Limits. A function f(x) has a limit L as x approaches c if we can get f(x) as close to c as possible but not equal to c. x is very close to, not necessarily at, a certain number c NOTATION:. 3 Ways to find Limits.

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1.2 Finding Limits

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  1. 1.2 Finding Limits Numerically and Graphically

  2. Limits • A function f(x) has a limit L as x approaches c if we can get f(x) as close to c as possible but not equal to c. x is very close to, not necessarily at, a certain number c NOTATION:

  3. 3 Ways to find Limits • Numerically - construct a table of values and move arbitrarily close to c • Graphically - exam the behavior of graph close to the c • Analytically

  4. 2 1) Given , find 3.61 3.9601 3.996001 3.99960001 4 2 4.004001 4.0401 4.41 4.00040001 4

  5. 1 2) Given , find 2.710 2.9701 2.997001 2.99970001 3 1 3.003001 3.0301 3.31 3.00030001 3

  6. 3. What does the following table suggest about a) b)

  7. Finding Limits Graphically • There is a hole in the graph. Limits that Exist even though the function fails to Exist

  8. One sided Limits notation Limits from the right Limits from the left

  9. 4) Use the graph of to find

  10. 5) Use the graph of to find

  11. 1 1 –1 –1 6) Use the graph of to find Does Not Exist – DNE

  12. 1 1 –1 –1 Limits that Fail to Exist • In order for a limit to exist the limit must be the same from both the left and right sides.

  13. 1 1 –1 –1 Limits that Fail to Exist • The behavior is unbounded or approaches an asymptote

  14. Limits that Fail to Exist • The behavior oscillates

  15. HOMEWORK Page 54 # 1-10 all numerically # 11 – 26 all graphically

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