Question

Help with limits of a function.
I'll add the picture.

Answer 1

Are those your answers in the little rectangles after each question in the diagram?

Answer 2

additional questions :

Answer 3

yes

Answer 4

wanna know if theyre good.

Answer 5

(a) isn't right... I think you just misread the graph. b and c are OK.

Answer 6

d and e look ok too

Answer 7

For the first question set:
a) 1
b)-2
c)DNE
d)2
e)0

Confused on these maybe? :o

Answer 8

oh, wait... maybe d and e approach (but never arrive at) 2 and 0, respectively? Is that it?

Answer 9

The overall lim as t -> 2 is DNE because the left and right side limits are different, but they do exist on their own sides.

Answer 10

thanks zepdrix :)

Answer 11

:D

Answer 12

oh yeah. a is -1
why is b = -2? its approaching from the right...and it has a hole if its coming from right.
and...d and e... they exist? it has holes on the graph.

So... the holes are answers after all..?

Answer 13

A function has a limit approaching from one side if it approaches a single answer. It doesn't matter about the hole... if it approaches arbitrarily closely based on increasingly closer t value inputs, that limit exists, even if at the actual t= value, the function has a hole

Answer 14

But for a "full" limit to exists, it must approach the SAME limit from both sides... again, it doesn't even matter if a hole exists at that precise point.

Answer 15

\[\lim_{t \rightarrow 0^-} g(t) \neq \lim_{t \rightarrow 0^+}\]
So certainly,\[\lim_{t \rightarrow 0} g(t) = DNE\]
As jake was saying. :D

When we're taking the limit from a specific side, we just care what value it's getting close to, without actually inputting 0.
So on your graph what that looks like is, what value am i approaching without actually touching the open circle.

Answer 16

I see. ok Thanks. I understand now.