/sci/ - Science & Math

[Anonymous No.4197217]

can you solve this

[Anonymous No.4197223]

0

[Anonymous No.4197225]

Yes, I can.

[Anonymous No.4197226]

0

[EK !EKFQOBUFnQ No.4197227]

erm, 0?

[Anonymous No.4197230]

L'hopitals x 2

[Anonymous No.4197245]

Anyone who can't should probably leave /sci/

[Anonymous No.4197255]

>solve
>a limit

[Anonymous No.4197258]

>>4197230
No need for L'hopital.. e^x grows faster than x^2, done.

[Anonymous No.4197270]

>>4197230

2x / e^x
=>2 / e^x
=>2 / ∞ ?

[Anonymous No.4197281]

Negative 0.

[Anonymous No.4197312]

>>4197258
Prove it without using L'hopital's rule.
In fact, define 'grows faster than' without referencing the question at hand.

[Anonymous No.4197322]

http://www.wolframalpha.com/input/?i=limit+as+x+approaches+infinity+of+%28x^2%29%2F%28exp%28x%29%29

[Anonymous No.4197327]

>>4197312
> define 'grows faster than' without referencing the question at hand.

for every positive value of x f(x) =e^x has a larger value than f(x) = x^2, furthermore f(x)-g(x) increases as x increases. This is what it means when a function is said to go to infinity faster.

[Anonymous No.4197328]

diferrentiate both denominator and numerator
<span class="math">\lim_{x \to\infty}{\frac{x^2}{e^x}} =\frac{\infty}{\infty}[/spoiler]

invalid
<span class="math">\lim_{x \to\infty}{\frac{2x}{e^x}}=\frac{\infty}{\infty}[/spoiler]
invalid
<span class="math">\lim_{x\to\infty}{\frac{2}{e^x}}=\frac{2}{\infty}[/spoiler]
hmm...
<span class="math">\frac{2}{\infty} = 0[/spoiler]

[EK !EKFQOBUFnQ No.4197329]

>>4197322
>limit as x approaches infinity of (x^2)/(exp(x))
holy shit, you can just write it like that and wolfram understands you!??

wolfram is fucking awesome, man.

[Anonymous No.4197332]

>>4197312
The question does not ask for that. Learn not to do unnecessary things.

[Anonymous No.4197364]

>>4197327
<div class="math">\lim_{x \to \infty}\frac{x^2+x}{x^2}=0</div>

for every positive value of x f(x) =x^2 + x has a larger value than g(x) = x^2, furthermore f(x)-g(x) increases as x increases. This is what it means when a function is said to go to infinity faster.

[GL !Bgpe2HycPk No.4197373]

>>4197364

0/10

[Anonymous No.4197383]

>>4197364
Oh fuck. >>4197327 got TOLD.

[Anonymous No.4197511]

>>4197332
Just saying 'e^x grows faster' isn't an answer, though.
I was making that point by asking the question. He managed to give a definition of faster growth that wasn't self referential, but he hasn't actually proven that e^x grows faster than x^2.
He said the hospital rule wasn't needed, and that's the part I challenge

[Anonymous No.4197535]

>>4197511
Can't you show that e^x grows faster than x^2 by showing that e^x-x^2 is strictly increasing for x>0

[Anonymous No.4197617]

>>4197373
What? That post just shows by example that the reasoning given by >>4197327 results in bullshit. Nothing wrong with that.

Why are you on this board if you don't understand such basic things?