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Bored?\[f:\mathbb R\to\mathbb R\mid e^{x\int f\left(x\right)}=\int f\left(x\right)\]Find:\[\lim_{x\to\infty}\left(f\left(x\right)\right)^x\]
 2 years ago
 2 years ago
Bored?\[f:\mathbb R\to\mathbb R\mid e^{x\int f\left(x\right)}=\int f\left(x\right)\]Find:\[\lim_{x\to\infty}\left(f\left(x\right)\right)^x\]
 2 years ago
 2 years ago

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LifeIsADangerousGameBest ResponseYou've already chosen the best response.0
The answer is 0. And I'm still bored _
 2 years ago

LifeIsADangerousGameBest ResponseYou've already chosen the best response.0
Haha! I'm right aren't I?
 2 years ago

badreferencesBest ResponseYou've already chosen the best response.1
No, lol, I hope that isn't a real question. XD
 2 years ago

LifeIsADangerousGameBest ResponseYou've already chosen the best response.0
_ You are clearly misunderstanding me < (see what I did there?) The answer is F.
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
i don't even understand the question
 2 years ago

badreferencesBest ResponseYou've already chosen the best response.1
Also, I should've specified a \(dx\) in the integrals, so it's clear they aren't an operation of \(f\). But I think you all knew that already.
 2 years ago

LifeIsADangerousGameBest ResponseYou've already chosen the best response.0
I didn't. So you misunderstood me again :D
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.0
what is \( dx \)? :P
 2 years ago

badreferencesBest ResponseYou've already chosen the best response.1
We're given conditions \(f:\mathbb R\to\mathbb R\) which means the function maps reals into reals. We know that \(\int f\left(x\right)\,dx=e^{x\int f\left(x\right)\,dx}\). We want to find the limit asked knowing this much.
 2 years ago

LifeIsADangerousGameBest ResponseYou've already chosen the best response.0
Could you repeat that?
 2 years ago

badreferencesBest ResponseYou've already chosen the best response.1
@LifeIsADangerousGame You are a snarky one, aren't you?
 2 years ago

LifeIsADangerousGameBest ResponseYou've already chosen the best response.0
It's my job. It's what I do.
 2 years ago

Mr.MathBest ResponseYou've already chosen the best response.1
@Ishaan94 I will come back to it later and see if I can do it. I feel tired now.
 2 years ago

Ishaan94Best ResponseYou've already chosen the best response.3
\[\mathsf{ \color{yellowgreen}{\text{Okay}}}\]
 2 years ago

Mr.MathBest ResponseYou've already chosen the best response.1
By taking ln of both sides we have \[x\int f(x)dx=\ln(\int f(x)dx)) \implies 1f(x)=\frac{f(x)}{\int f(x)dx}\] \[\large \implies f(x)=\frac{\int f(x)dx}{\int f(x)dx+1}.\] Because \(\int f(x)dx>0\), we have \( 0<f(x)<1\). Hence \[\large \lim_{x\to \infty} (f(x))^x=0.\]
 2 years ago

Ishaan94Best ResponseYou've already chosen the best response.3
Oh, I did the same but read above, badref rejected Zero as the answer :/
 2 years ago

karatechopperBest ResponseYou've already chosen the best response.0
ISHAAN GET IN CHAT IF U R NOT HELPIN...
 2 years ago

karatechopperBest ResponseYou've already chosen the best response.0
:D intrestin lookin R u got there
 2 years ago

Mr.MathBest ResponseYou've already chosen the best response.1
Well, he/she should post the answer then.
 2 years ago

Ishaan94Best ResponseYou've already chosen the best response.3
Post the Answer! Post the Answer! Post the Answer!
 2 years ago

badreferencesBest ResponseYou've already chosen the best response.1
Lol, I actually mistyped the question. I think the answer for this is actually \(0\), my bad.
 2 years ago

Mr.MathBest ResponseYou've already chosen the best response.1
What is the question then?
 2 years ago
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