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when

when . (1) Domain of f(x) : . (2) Graph of f(X):. Graph of f(x):. Can we “recover” the value at x=0?. as x gets closer and closer to 0 in any way, without equaling 0, f(x) gets closer and closer to 1. ex:. exist?. Does . Graph of g(x):. as x gets closer and closer to

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when

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  1. when (1) Domain of f(x) : (2) Graph of f(X):

  2. Graph of f(x): Can we “recover” the value at x=0?

  3. as x gets closer and closer to 0 in any way, without equaling 0, f(x) gets closer and closer to 1

  4. ex: exist? Does

  5. Graph of g(x):

  6. as x gets closer and closer to a in any way, without equaling x=a, g(x) gets closer and closer to L Same, but with x > a always Same, but with x < a always

  7. For the limit to exist and equal L: Both must exist and equal L In particular, the right and left limits must equal each other

  8. What happens with the limits at x = -2, 1, 2, and 3?

  9. Does exist? x=0 is not in the domain!! 0.5 0.95885108 -0.3 0.98506736 +0.1 0.99833417 -0.0.1 0.99998333 +0.001 0.99999983

  10. However, 0.0001 0.2000 -0.00005 0.0000 (??) 0.00001 0.0000 (??) What’s going on?

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