Question

What is the limit of e^x as x approaches negative infinity?

Answer 1

\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~-\infty}~e^x}\)

Answer 2

you can tell just by logical analysis.

Answer 3

oh, duh.... zero?

Answer 4

yes, \(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~-\infty}~e^{x}=0}\)

Answer 5

lol... well i'm working with \[\lim_{x \rightarrow -\infty}\frac{ e^x+e ^{-x} }{e^x-e ^{-x} ? }\]

Answer 6

oh, that is a bit different, or at least looks different.

Answer 7

what I thought was that I'm suppose to divide each term by \[e^x\] but, i'm doubting myself

Answer 8

yes, I don't think it would work, because then you get (roughly)\[\frac{0 +( \infty )}{0-(\infty)}\]

Answer 9

which would make the answer negative infinity?

Answer 10

well, actually, it can work....

Answer 11

let me think

Answer 12

yes, it works

Answer 13

then you get -1

Answer 14

and wouldn't it be \[\frac{ 1+\infty }{1-\infty }\]?

Answer 15

well, the limit of e^x as x approaches - infty is 0.
isn't it so ?

Answer 16

oh oh, got it

Answer 17

so, if you separate the whole limit into a bunch of limits, you get
(- infty) / (+ infty) which would be -1

Answer 18

and these infinities here are in/de creasing with the exact same maginute

Answer 19

magnitude*

Answer 20

I might be here a bunch, I got really behind due to a brutal winter that my immune system does not like, thanks Solomon

Answer 21

the school and work systems don't like it either .... a couple of snowflakes fell (which they called a "snowstorm") and the city was paralyzed.

Answer 22

... have a warm weather :)

Answer 23

lol, you won't find that in Cleveland.... not for a while.... thanks again! peace

Answer 24

would be easier to use `\(\large\color{blue}{ \heartsuit }\)` which gives: \(\large\color{blue}{ \heartsuit }\) .

you can change the color "blue" to "black", "green", "magenta" or any other.