Question

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

Answer 1

i have attached the graph

Answer 2

its an empty graph

Answer 3

one sec

Answer 4

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

Answer 5

sure one sec

Answer 6

there the pic is attached

Answer 7

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

Answer 8

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

Answer 9

to prove:

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

Answer 10

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

Answer 11

do you have pdf

Answer 12

no

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

And they aren't both f(-2)

Answer 17

err f(2)

Answer 18

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

Answer 19

k thats one

Answer 20

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)

Answer 21

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

Answer 22

sprinkle in some epsilons and deltas for good effect :)

Answer 23

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

Answer 24

we can see that there for every epsilon in the neighborhood of L can be produced by a delta such that 0<|x-c|<d in the neightborhood of 2

Answer 25

forget this problem adding a new one