Question

How do you find this limit? (will be attached)

Answer 1

Back :D

Answer 2

WOO! :) hold up a sec while I write out the limit function thing XD

Answer 3

xD

Answer 4

In terms of a rigorous method of going about it I couldn't tell you, but think of it this way. Who would win in a race to infinity, x^4 or e^x?

Answer 5

When you plug in infinity for x I mean, lol.

Answer 6

Um, x^4?

Answer 7

Calculus makes me feel extremely stupid.

Answer 8

Nah, I just phrase it in a bad way :P
\[\infty ^{4} \]
\[e ^{\infty}\]
Any idea which one you think would climb to infinity faster?

Answer 9

Now I think it's e^infinity O.o UGH. Which is it supposed to be?

Answer 10

It is e^infinity. So we're used to looking for the degree, but in this case we really don't have one. So in order of lowest to highest, we would have this:

\[\infty ^{n}<n ^{\infty}<\infty!\]
So infinity to a power is less than a number that has a power of infinity, but is less than infinity factorial. So in this case, your higher degree, so to speak, would be in the denominator. Which means the fraction becomes what? :P

Answer 11

0?

Answer 12

Yep :P which leaves what remaining? :o

Answer 13

0-1, so it equals -1 :)

Answer 14

yep, thats your limit.

Answer 15

AWESOME. You're legit like my favorite person ever right now. I spent all class staring blankly at this worksheet and now I've got around half of it done because of you!

Answer 16

Lol, np. Limits aren't that bad really. Oh, the next thing you do after limits is derivatives. I can help ya out with that. Now, it may not make sense because I teach it in an odd way, but I do have some files that have mini examples on how to do derivatives.

Answer 17

I'll definitely come to you when we start with those :) I think the main problem was just the fact that she wasn't in class today to guide us from the very basic lesson she taught us to these problems.

Answer 18

Do you know what to do when it turns out the limit isn't of a fractional function? Like, one is a polynomial, and another has e^some power of x

Answer 19

Do you have an example?

Answer 20

One of them is \[e ^{\frac{ 1 }{ x }}\] and the other is \[-x ^{2}+4x-6\] the first is for x approaching infinity, the second is x approaching negative infinity.

Answer 21

What do you do when x approaches negative infinity? What changes?

Answer 22

Well, what does 1/x become as it goes to negative infinity?

Answer 23

0, but that one is for a approaching positive infinity. But it's still the same, isn't it?

Answer 24

Yep, instead of the numbers becoming something like .00000000001, they just become -.00000000001 and get closer to 0 from the other side. So then that just leaves you with e^0 which is 1.

Answer 25

Awesome. That's what I got :) Okay, I thought by figuring out how to solve that one I'd be able to figure out how to solve \[-e ^{-2x}+1\] but I can't seem to figure it out

Answer 26

For this one it helps to just know what the e^x function is actually doing. Do you know the range of the e^x function?

Answer 27

No, I'm still not entirely sure what e even is. Everytime I see it I just want to get rid of it by taking the natural log of it XD

Answer 28

Lol, well its the inverse of that. So this is e^x and lnx:



e^x always goes through (0,1)
lnx always goes through (1,0) Now as you can see, e^x has a range of (0,infinity). So if we make x become negative infinity, we see that e^x goes left left left left to 0. So:

\[-e ^{-2\infty}=-0 =0\] And then you have the random + 1 there xD