homework (calc)

do your homework you faggot

and go to college

unless you wanna flip burgers for the rest of your life

>>268258
Dude, you've got a whole year to figure this out. I'm sure you can learn what you need to in that span.

What is the definition of x! trying to do? What class is this again? This is way above my DiffEq education.

> 1 < (x-1)!(x+1)/(x+1)! ∀x > 1
Literally never seen this syntax before
But shouldn't this be the same as
> 1 < (x-1)!/(x+1)! ∀x > 1

(because 1/x! = (x+1)/(x+1)!)

oh, that was a type forgot to mention that, couldn't correct it on pdf, it's not due in 2018

well, the upside down "A" thingie means "for all"

>>268258
something something gamma radiation

>>268282
I'm sorry if I'm not clear but english isn't my first language.

So x! is defined as x*(x-1)*(x-2)...3*2*1.
The equation with x! given at the top just state that
x! = (x+1)*x*(x-1)...3*2*1 / (x+1),
where the first part is just (x+1)! written out. Then by letting (x+1) go out you end up with the definition og x!.

You're nearly right about equation B, but you have (I guess) mistakenly inserted 1/(x+1)! instead of 1/x!. Now you should have
1 < (x-1)!/x!.
By remembering the definition of x! you should be able to see that (x-1)!/x! = 1/x (which can be written to match the top equation (x-1)! = x!/x).
Therefore B state that 1 < 1/x for all (values of) x > 1, which you should be able to determine if it's true or false.

i meant that I know the answer is B, i kinda get why in general 1 would actually be greater than that. Now I'm just confused on how the professor got the bounds of "for all x >1" part

>>268258
>>268479
>>268493

I think that this test may actually be about using ONLY the given statements and basic mathematical logic to prove each statement in turn, without using ANY other information about the properties of the gamma function and the factorial.

So, for the first one, you may try:
(x-1)!*(x+1)/(x+1)! =
= (x-1)!/[(x+1)!/(x+1)] (associativity)
= (x-1)!/x! (using 2 on denominator) =
= (x!/x)/x! (using 2 on numerator) =
= 1/x * x!/x! (associativity) =
= 1/x * 1 = 1/x, for x>0 (because 1/x is not defined for x=0)

Therefore, A is true.

For the second one, since x>1>0, you can use A on the right hand side to get 1 < 1/x for x>1, which is never true, so B is false.

You can use 1 and 4 to get gamma(x+1)>gamma(x), from that you get x!>(x-1)!, ant then you can solve inequalities. This should get you started.

>>268493
For A, 1/x is undefined if x=0. C is false for x<=1, because it is equivalent to 1>1/x. D is C multiplied by the numerators. For E, note that the second given equation x!=(x+1)!/(x+1) is not defined for x=-1, since that would divide by zero.

Thanks guys! I wasn't sure about my choice of B, but now I feel like I can justify it

>>268282
Oh, I was totally misreading the order of operations there. Yeah, I've seen this syntax before.

I know ∀x means "for every x" but with the additional "∀x > 1" I thought it was saying like "1 < n > 1" which is... redundant