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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 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 • Numerically - construct a table of values and move arbitrarily close to c • Graphically - exam the behavior of graph close to the c • Analytically
2 1) Given , find 3.61 3.9601 3.996001 3.99960001 4 2 4.004001 4.0401 4.41 4.00040001 4
1 2) Given , find 2.710 2.9701 2.997001 2.99970001 3 1 3.003001 3.0301 3.31 3.00030001 3
Finding Limits Graphically • There is a hole in the graph. Limits that Exist even though the function fails to Exist
One sided Limits notation Limits from the right Limits from the left
1 1 –1 –1 6) Use the graph of to find Does Not Exist – DNE
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.
1 1 –1 –1 Limits that Fail to Exist • The behavior is unbounded or approaches an asymptote
Limits that Fail to Exist • The behavior oscillates
HOMEWORK Page 54 # 1-10 all numerically # 11 – 26 all graphically