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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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slide1

when

(1) Domain of f(x) :

(2) Graph of f(X):

slide2

Graph of f(x):

Can we “recover” the value at x=0?

slide3

as x gets closer and closer to

0 in any way, without equaling

0, f(x) gets closer and closer to

1

slide5

ex:

exist?

Does

slide7

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

slide8

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

slide10

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

slide11

However,

0.0001 0.2000

-0.00005 0.0000 (??)

0.00001 0.0000 (??)

What’s going on?