Prove that the graph is continuous or not continuous at x = 2.

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- anonymous

Prove that the graph is continuous or not continuous at x = 2.

- katieb

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- anonymous

i have attached the graph

##### 1 Attachment

- amistre64

its an empty graph

- anonymous

one sec

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- amistre64

and a picture is better, since not everyone has microsoft office

- anonymous

sure one sec

- anonymous

there the pic is attached

##### 1 Attachment

- anonymous

Or even if they do have office, opening docs from unknown sources can sometimes be problematic.

- anonymous

f(2) exists (infact f(2) = 4

- amistre64

to prove:
the lefthand limit has to equal the right hand limit at x = 2

- amistre64

how to prive that without actual functions? my best guess is just to point to it on the graph and say, "see! right there"

- anonymous

do you have pdf

- amistre64

no

- anonymous

i can send you a similar graph which the teacher gave us to review with

- amistre64

i got the picture of the graph now; its just that there is no peicewise function defining the curves

- anonymous

You can see what the left and right hand limits are by looking at the graph.

- anonymous

And they aren't both f(-2)

- anonymous

err f(2)

- anonymous

\[\lim_{x \rightarrow 2^+}f (x)=5\neq \lim_{x \rightarrow 2^-}f(x)=2\]
Hence f is not continuous at \(x=2\).

- anonymous

k thats one

- anonymous

A function is continuous about a point p if and only if p in in the domain of f, and
the limit from the left = the limit from the right = f(p)

- anonymous

f(2) exists (in fact f(2) = 4
is this correct

- amistre64

sprinkle in some epsilons and deltas for good effect :)

- anonymous

one second i will attach the sample graph she provided i think thats how she wants the answers

- amistre64

we can see that there for every epsilon in the neighborhood of L can be produced by a delta such that 0<|x-c|

- anonymous

forget this problem adding a new one

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