Question

what is the limit of 2x/x+3 as x approaches -3 from the left

Answer 1

graph it

Answer 2

I'd rather not be dependent on my calculator

Answer 3

Well then take a random, educated guess

Answer 4

xD

Answer 5

And here come Psymon..

Answer 6

no really

Answer 7

Well, because there is no way to eliminate that x+3 denominator, this means that there must be an asymptote at x = -3. If there was not an asymptote, thered be a way to eliminate the x+3 denominator to make the limit exist. SO that being said, we know this graph will go to infinity or negative infinity at x = -3. So we just need to check a couple values of x as it approaches -3 from the left. So from the left of -3 means -6, -5, -4, etc. So if we test -4:
\[\frac{ 2(-4) }{ -4+3 }= 8\]So now we will test -3.5, even closer to -3 and see if our function value decreased or increase. Plugging in -3.5 I get:
\[\frac{ 2(-3.5) }{ -3.5+3 }= 14 \]Well, our function value shot up. So for sure that as we approach -3 from the left, we will go to positive infinity.

Answer 8

^

Answer 9

So you could say there isn't a limit?

Answer 10

It kind of depends on what section of the text you are in. Earlier on in an intro to limits, you would say does not exist. But once you get introduce to limits to infinity, you would say the limit is positive infinity. It all depends on where you actually are in your calculus course.

Answer 11

If you're in calc there is a limit, if you're in pre-calc you must likely take DNE as an answer

Answer 12

*most

Answer 13

We were just introduced to limits on thursday, so for now im going to put does not exist. thanks slugger

Answer 14

Sure ^_^

Answer 15

._.

Answer 16

Cheer up @Luigi0210 ^_^