Question

more continuity c:

Answer 1

Find the indicated limit, if it exists.

Answer 2

So, whats the limit as we approach 0 from the left? Which part of the piece-wise function would we use?

Answer 3

i have no idea. i cant even figure out how to put this into my calculator .-.

Answer 4

So, if we approach zero from the left, we're approaching when x is negative.

If x is negative, which part of the function would we use?

Answer 5

the second part

Answer 6

No, the first.

That notation means:
When x "is less than" 0, f(x) = 5x-8
When x "is greater than or equal to" 0, f(x) = |-4-x|

So, when approaching from the left (from the negative side), we'll use the first equation.

Since there isn't anything that would stop us from having x=0 in that equation (we aren't dividing by x anywhere, for example), the limit is just what you get when you plug in 0 for x.
\[\lim_{x \rightarrow 0^-}f(x) = 5(0)-8 = -8\]
So, the left-hand limit is -8.

What would we do to find the limit from the right hand side?

Answer 7

itd be |-4-(0)| =|-4|=4

Answer 8

Yep!

Are the two limits the same? If they are, then the limit exists, and that's the answer.
If they are not, then the limit does not exist.

Answer 9

they dont match so they arnt the same right?

Answer 10

Correct. So the limit does not exist.

Answer 11

okay thank you c:

Answer 12

Does it make sense?