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Mathematics 7 Online
OpenStudy (anonymous):

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.

terenzreignz (terenzreignz):

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

OpenStudy (anonymous):

Yes

OpenStudy (mandre):

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

OpenStudy (anonymous):

Can you explain how you got the answer, please?

terenzreignz (terenzreignz):

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

OpenStudy (mandre):

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

OpenStudy (anonymous):

Yeah. @terenzreignz

terenzreignz (terenzreignz):

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

terenzreignz (terenzreignz):

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

terenzreignz (terenzreignz):

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

OpenStudy (anonymous):

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

OpenStudy (mandre):

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

terenzreignz (terenzreignz):

POSITIVE infinity @pokemonmaster96

terenzreignz (terenzreignz):

Make sure to make that distinction

OpenStudy (anonymous):

Yeah, positive infinity.

OpenStudy (anonymous):

Thank you, everyone. :)

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