Limits

[boreal forge]

How do i do these types of limits?

[radiant tundra]

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[viscid oracle]

direct evaluation but you have to be a bit creative

like, whats $e^\infty?$

[sour nebula]

!𒐪 ɹɐupoɯ⇂ㄥ8𝟝 𒐪!

[boreal forge]

infinity

[viscid oracle]

yup

and whats $3+\infty$

[sour nebula]

!𒐪 ɹɐupoɯ⇂ㄥ8𝟝 𒐪!

[boreal forge]

infinity ?

[viscid oracle]

yup

that will get you a few places for now

i should probably warn you here that uhhh what do you think $\frac{2\infty}{\infty}$ evaluates to?

[sour nebula]

!𒐪 ɹɐupoɯ⇂ㄥ8𝟝 𒐪!

[boreal forge]

uhh

2?

[viscid oracle]

so its not

you can never cancel out infinity

[boreal forge]

oh

[viscid oracle]

the way to do this is you realize $2\infty=\infty$, and $\frac{\infty}{\infty}$ is an indeterminate form (youll learn this later if you havent already)

[sour nebula]

!𒐪 ɹɐupoɯ⇂ㄥ8𝟝 𒐪!

[viscid oracle]

and the reason why you cant cancel infinity is some infinities are bigger than others

[boreal forge]

ohh

[viscid oracle]

but yea thats some knowledge youll need in the future

for now for these you can direct sub infty into the thing

[boreal forge]

ohh okay

thank you

[viscid oracle]

yw

try the questions out and if you have issues feel free to ask more questions

[boreal forge]

wait for e^-2xinfinity

[viscid oracle]

if not you can just close

[boreal forge]

would that equal -infinity ?

[viscid oracle]

does e^ anything equal a negative number?

[boreal forge]

ohhh right

[viscid oracle]

well, e^real

[boreal forge]

thank you

ill try them now

[viscid oracle]

gl!

[obsidian mason]

Technically it's because some functions grow faster than others. Transfinites have nothing to do with that.

[boreal forge]

i still dont get it 😭

i get why a) is infinity

but i dont get why

b) equals - inifinity

and why c) is 7

wait nvm i get b

its cause its 5 - infinity

which is - infinity

[viscid oracle]

show your work for c

[boreal forge]

7 - e^(-2 x infinity)

ohh wait

nvm

[obsidian mason]

You know that lim_(x -> inf) e^x = inf, right?

So you can just use algebra and variable substitution to generate an e^x term.

Or an e^whatever term, in the case of variable sub.

[boreal forge]

+close

[rocky lynx]

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