Question

Use the given graph to determine the limit, if it exists.


Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x..

Answer 1

Something really important to note:

\[\lim_{x^{+} \rightarrow n} = \lim_{x^{-} \rightarrow n}\]

Answer 2

\[\lim _ {x \rightarrow 2^{-}} \lim_{x \rightarrow 2^{+}}\]

Answer 3

the limit as x approaches a number from the left must be equal to the limit as x approaches the number from the right

Answer 4

The limit doesn't exist because as x approaches the number from the left and right you see that there are two different values. at 2.

but another thing: the function isn't defined at 2 either because of that circular hole. that's called a discontinuity

Answer 5

I think the function is defined at 2. but not equal to lim as x->2^{-,+}

Answer 6

these are my options..

1; 1

3 ; -3

does not exist ; does not exist

-3, 3

Answer 7

they want to know the lim as x-> from left and right

if the \[\lim_{x \rightarrow 2^{-}} \cancel{= }\lim_{x \rightarrow 2^{+}}\]
then the full lim as x-> (2) doesn't exists but the limt from right and left exist

Answer 8

as @Nnesha said, I think we can agree that the limit does not exist.

Answer 9

yes but the full limit does not exist
lim from right and left DOES exist

Answer 10

not arguing there

Answer 11

i noticed that there are three different values for x at 2 so that was why i thought it was not a function

Answer 12

\[\large\rm \lim_{x \rightarrow 2^{-}}\]\ they are looknig for y value when x approch 2 from left