Question

Determine the infinite limit? (I have to present it in class. can I have an explanation please).
lim + x + 2
x->-3 ------- =
x + 3

Answer 1

+
x approach -3

Answer 2

\[
\lim_{x\to -3^+}\frac{x+2}{x+3}=
\]

Answer 3

@micalg do you understant?

Answer 4

well as we aprroac-3 from the right we will have negative on top, and positive on bottom, but the bottom will tend to 0 as we get close
so we have -/+ but the top is a constant,
so limit = -infinity

Answer 5

Fill out a chart:

Answer 6

yah I think I started to

Answer 7

Also you can use epsilon delta to prove it: \[
\forall N, \exists \delta: \\
\forall x \quad 0<x-(-3)<\delta \implies \frac{x+2}{x+3}<N
\]

Answer 8

it does not converge @wio
so you would need\[\forall \space M,\exists\epsilon>0\space st\space |x-(-3)|<\delta \implies f(x)>M\]

Answer 9

and its not N, unless you are saying that N is in R, but we never say that...

Answer 10

This is a one sided infinite limit. It has a particular definition. I might have made a minor error.

Answer 11

if it has a limit, this does not.

Answer 12

But there should not be any absolute value signs for this type of limit.

Answer 13

evrey definition I know of limits has abs value...

Answer 14

The one-sided limit does exist in this case.

Answer 15

There are about 12 variations on the definition of a limit to account for things like one-sided limits, infinite limits, limits of sequences, etc.

Answer 16

Actually much more than 12 variations. Anyway the general definition takes a lot of math that is not introduced in calculus to write out well.

Answer 17

its not that bad, I was simply saying that you are forcings things to be smaller than a natural number, it should be all real numbers

Answer 18

I didn't mean to say anything about natural or real numbers.

Answer 19

so it would be
\[\forall M , \exists\delta>0, st\space -\delta<x<a\implies f(x)>m\]

Answer 20

we are showing divergence so f(x)<N makes no sense...

Answer 21

I intially said \(f(x) < N \) is because before you said \(-\infty\).

Answer 22

But since it is going towards \(\infty\) then yes, in this case you'd do \(f(x)>N\)