Question

Help with limits for a medal?

Answer 1

No question.

Answer 2

Im attaching the file

Answer 3

Still no question

Answer 4

Use the graph to find the limit and determine the continuity of the function.

Answer 5

Sorry about that. My internet is giving me some troubles.

Answer 6

What limit?

Answer 7

np the servers here are funny sometimes.

Answer 8

Just a sec. It's not letting me post them

Answer 9

Hah! Got it!

Answer 10

Right, this is what I figured.

Ok as you walk along the graph from left to right there is an obvious problem at \(x=-1\). What value do you approach(y value) as you get closer to \(x=-1\)

Answer 11

There's a hole in the graph

Answer 12

what value is y when you approach from the left?

Answer 13

2

Answer 14

so \(\lim_{x\rightarrow c^{-}}f(x)=2\)

What about from the right?

Answer 15

It gets closer to 0

Answer 16

Yep

so \(\lim_{x\rightarrow 2^{+}}f(x)=0\)

Answer 17

now does \(2\ne 0\)?

Answer 18

Yes, 2 doesn't equal zero.

Answer 19

obviously not, thus \(\lim_{x\rightarrow c}f(x)\) does not exist

Answer 20

That was much easier than I expected.

Answer 21

now, since we cant just fill in one point and make it continuous, i.e. there is no one point that we can add so that we can draw the entire graph without lifting the pencil

and thus is does not have a removable discontinuity .

Answer 22

I see now. Thank you! :)

Answer 23

np