13.1 Finding Limits Using Tables and Graphs

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Presentation transcript:

13.1 Finding Limits Using Tables and Graphs

As x gets closer to c, but remains unequal to c, the corresponding values of f(x) get closer to N.

Example (Left) (Right)

y 8 (2, 7) 6 4 2 x 2 4 6

Use graphing utility to find

Does the limit exist at x = 1 if so what is it?

One-Sided Limits

RECAP Definitions This means that as x gets closer to a, but remains less than a, the corresponding values of f(x) get closer to L. This means that as x gets closer to a, but remains greater than a, the corresponding values of f(x) get closer to L.

Equal and Unequal One-Sided Limits One-sided limits can be used to show that a function has a limit as x approaches a: One-sided limits can be used to show that a function does not have a limit as x approaches a:

3 1 -1 -3 -2 -1 -3 No limit.