Question

lim x > -3 h(x)
I was wondering if the answer is 4 or if it does not exist because it's a sharp corner/curve?

Answer 1

And that is a graph of h in the picture right?

Answer 2

Yes

Answer 3

If that is h, h' would not exist at -3 because of the hole. But the limit as x approaches -3 of h' would also not exist because of the sharp turn (you have different slope functions on each side of -3)

however you are talking about h and h is as is the limit is 4 because as we approach -3 from both sides that is what the y values approach (we don't care what happens at -3, just around)

Answer 4

Do you understand?

Answer 5

From the graph we can tell using left values of x as we get close to x=-3, the y-values get close to 4.
From the graph we can also tell using right values of x as we get close to x=-3, the y-values get close to 4.

Answer 6

so bottom line the limit as x approaches -3 does not exist

Answer 7

@myininaya

Answer 8

No no. That isn't what I said. Unless you are talking about h'?

Answer 9

But you said you were talking about h.
The limit is only concerned about what happens around a number.
From both sides of x=-3 the y-values tend to 4 so the limit is 4.


If you were talking about h' then we would be concerned about that sharp turn there at x=-3 and the limit would not exist at x=-3.

Answer 10

In symbols, what I'm saying is:
\[\lim_{x \rightarrow -3}h(x)=4 \text{ but } \lim_{x \rightarrow -3}h'(x) \text{ does not exist because of the sharp turn in h at x=-3}\]

Answer 11

I included the information about h' because you talked about sharp turns and if you needed to be concerned with them. I'm telling you when you do to be concerned about the sharp turns.

Answer 12

ok thank you so much

Answer 13

For example if we have g(x)=|x|
\[\lim_{x \rightarrow 0}g(x)=0 \text{ but } \lim_{x \rightarrow 0}g'(x) \text{ dne} \]

Answer 14

Do you know why the limit would not exist for g' at x=0?

Answer 15

but g'(x) looks like


The sharp turn on g gives us two different slope functions on both sides of x=0
and