Question

Can somebody help me figure out the limit as x approaches infinity from the left of (7/x - x/2)?

Answer 1

combine the two fractions

Answer 2

Did that and got DNE.

Answer 3

well, DNE is technically correct, but some people consider the case +/- infinity to be the limit of the function

Answer 4

Well, webassign won't take either of those answers. I have tried them both.

Answer 5

did you try *negative* infinity?

Answer 6

yeah

Answer 7

my question is, what does "approaches infinity from the left" mean?

Answer 8

hmm right

Answer 9

you can go to \(\infty\) only from the left

Answer 10

so maybe there is a typo in the question

Answer 11

Okay, it wanted infinity... that seems like half an answer to me.

Answer 12

I gather he meant \(\Large \bf lim_{x\to + \infty^-}\)

Answer 13

lol

Answer 14

my guess is it is
\[\lim_{x\to -\infty}\]

Answer 15

in which case \(\infty\) would be the right answer, assuming you take that as a limit

Answer 16

Yeah, you are right. I hate limits. Can you explain, using rules of infinite limits why, DNE wouldn't be the answer?

Answer 17

it would be, unless you admit \(\infty\) or \(-\infty\) as an answer
it is really talking about "end behavior"

Answer 18

I'm guessing DNE is preserved for the limit of a function of at a single point.

Answer 19

So, it being a one sided limit is the issue. If it were just the limit as x approaches infinity from both sides, it wouldn't exist.

Answer 20

@jcates00 because you're approaching a value that's never defined, since -infinity would be by definition just that, thus it's \(\bf DNE \iff -\infty\)