Question

Determine if a limit exists. If the limit approaches infinity or negative infinity, state which one the limit approaches.
The limit of... 1/(x+1) as x approaches -1^+
Thanks.

Answer 1

Sorry, this limit?
\[\huge \lim_{x\rightarrow -1^+}\frac{1}{x+1}\]

Answer 2

Yes

Answer 3

The limit does not exist as the limit approaches positive and negative infinity.

Answer 4

Can you explain how you got the answer, please?

Answer 5

Not negative infinity @Mandre
The denominator goes to zero, so you can bet that the limit goes to infinity, right, @pokemonmaster96 ?

Answer 6

I read it from the graph. Trying to figure out the mathematical way.

Answer 7

Yeah.
@terenzreignz

Answer 8

Okay, so to figure out where it goes, as x goes to -1, we'll check values really close to -1, say, -0.5
\[\Large \frac1{-0.5+1}=\frac1{0.5}=2\]

Answer 9

Let's go even closer, say, -0.9999
\[\Large \frac1{-0.9999 + 1 }=\frac1{0.0001}= 10000\]

Answer 10

And so on, as you get closer and closer to -1, the function just gets infinitely bigger, hence it goes to positive infinity

Answer 11

So, it's approaching infinity!
:D Thank you

Answer 12

It's approaching from the right so it actually only approaches positive infinity.

Answer 13

POSITIVE infinity @pokemonmaster96

Answer 14

Make sure to make that distinction

Answer 15

Yeah, positive infinity.

Answer 16

Thank you, everyone. :)