Question

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

Answer 1

What are your choices?

Answer 2

you see it approaches different value from 2 sides

Answer 3

DNE
1; 1
-2; 3
3; -2

Answer 4

but, a one sides limit does exist,.

Answer 5

yea, because it is shaded right?

Answer 6

\[\lim_{x \rightarrow 2}f(x)~~DNE\]

Answer 7

brostep, wha?

Answer 8

so the left side doesn't exist?

Answer 9

\[why?~~~\lim_{x \rightarrow 2}f(x)~~DNE,~~~beca use,~~~~\lim_{x \rightarrow 2^+}f(x) \neq \lim_{x \rightarrow 2^-}~f(x).\]

Answer 10

a side DOES exist.

Answer 11

one sides limit almost always does exist, I guess, unless you are too far off, like

Answer 12

oh, alright

Answer 13

yes, the left sided limit is just the line that comes from the left, and as x approaches 2 , the f(x) approaches?

Answer 14

3

Answer 15

yes.

Answer 16

and from the right side?

Answer 17

-2

Answer 18

there you, and this what it means that
\[\lim_{x \rightarrow 2^+} f(x) \neq \lim_{x \rightarrow 2^-} f(x) \]

Answer 19

but that only means, again, that
\[\lim_{x \rightarrow 2} f(x) ~~~DNE\]

But,
\[\lim_{x \rightarrow 2^+} f(x)~~~ex ists\]and\[\lim_{x \rightarrow 2^-} f(x)~~~ex ists\]

Answer 20

1 sides limit exists, 2 sides limit does not.
Done.

Answer 21

Ok, Thank you Very Much!

Answer 22

yw