Question

Which of the following statements are true?


I. If a new series is found by differentiating a known series with included endpoints, those endpoints might not be included in the new series.

II. If a new series is found by differentiating a known series with included endpoints, those endpoints will never be included in the new series.

III. If a new series is found by differentiating a known series without included endpoints, the endpoints in the new series will also not be included.

Answer 1

What do you think?

Answer 2

I only
II only
I and III
II and III

Answer 3

Well with the example of ln(1+x), it has a interval of (-1,1] but the derivative of it is 1/(x+1) but that doesn't have an interval

Answer 4

It doesn't converge

Answer 5

Okay, so what's your guess? l. or ll. or lll.?

Answer 6

Well I pick, just I only and I got it wrong

Answer 7

I say I and III since that never seems to be make a wide conjecture that probably has an example that I can't think of

Answer 8

Oh wait, you're supposed to choose 2 choices?

Answer 9

For II when it says "never"

Answer 10

Yeah, here are the options:


I only
II only
I and III
II and III

Answer 11

I think you are correct :)

Answer 12

l and lll

Answer 13

Yep! Thanks

Answer 14

No problem! :)