Why is it logically possible to randomly divide variables like

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>>8391539
Because you're just multiplying by 1:
[eqn]\frac{\frac{1}{r}}{\frac{1}{r}} = 1.[/eqn]

a/b = (a/c)/(b/c) = (a/b)(c/c) = a/b

>>8391539
>Why is it logically possible to randomly divide variables like that?

Are you for real?

a/b = (a/k)/(b/k)
because
(a/k)/(b/k) =
(a/k)*(k/b) =
ak/kb =
a/b

What rules am I using? Only one rule: (R,+,*) is a field.

>>8391551
What makes the 7 eligible to be divided by are?

>>8391593
7 is a real number
r is a real number

7/r is a real number

The answer is: why the fuck not?

The fact that this turns out to help you find this limit is mere coincidence.

>>8391601
Then how do I know what will "coincidentally" will solve the expression?
"why the fuck not" is not reliable.

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>>8391539
>>8391593
>>8391614
lazy bait, do not respond

>>8391732
I legitimately do not understand. Why do you fuckers act act like you and math are so logical, and when someone asks a question you insult them? This is why I find stemfags disgusting.

>>8391614
>Then how do I know what will "coincidentally" will solve the expression?
>"why the fuck not" is not reliable.
>How do I know

You don't.

You were given a problem. The thing is that you were also given the illusion of simplicity. By seeing such a short solution, without the actual trial and error the guy who solved it went through, you think that there is an immediate formula that tells you what to divide.

There isn't.

Let me tell you how I would approach that limit:

It is a limit to infinity. From previous experience (here I am telling you to fucking practice) I know that these limits are usually solved by finding which values go to 0.

For example. The simpler limit x^2/(x + x^2) looks weird but you can turn that x into a 0 by dividing everything by x^2 which yields

1 / (x^-1 + 1)

this is a good form because one of the elementary theorems of limits is that the limit as x approaches infinity of x^-1 is 0 so now we got it. The limit is 1.

So you do the same. You need to divide everything by something that will turn things into 0.

To be fun, I will pretend I am retarded and also try r^2. This will yield (skipping steps)

(r^-1)/(2r^-1) = (1/2)(r^-1/r^-1) = 1/2

Look at that. I arrived at the same conclusion by dividing by something else.

So the answer is that you don't really need to divide by an specific thing You just need to think about one thing:

How can I turn as many terms as I can into 0s that I can then just forget about so that I can deal with an easier limit?

>>8391824
It's more cause you're too lazy to find the answer and you demand it from us. By the way, the only explanation I have is what my math teacher would say, "because I can"

they are multiplying by 1, choosing sinr/r/sinr/r just because it cancels out terms, they could choose literally anything as long as it simplifies to 1.

>>8391539
You know you're supposed to be at least 18 to be on 4chan right?

Also, for help with homework: read the fucking sticky

Also, you're not randomly dividing, you're dividing by the highest power in the expression due to the fact that evaluating a limit as it approaches infinity only applies to the highest powers in the numerator and the denominator. For example 1/x is 1/infinity which is 0

Eventually, when you get out of precalculus, none of this explaining will be necessary because it's so fucking simple

>>8391843
If you're not gonna answer then don't reply.

I tried to solve this for 2 hours and couldn't so I went to the solution and still couldn't understand it.
BTW you must have a shitty math teacher.

>>8391862
>BTW you must have a shitty math teacher.

Not him but here we don't have teachers, we have professors.

They also don't teach us calculus, they teach us algebraic topology and topological algebra.

>>8391842
why is 7/r=0?

>>8391882
Because 7/infinity is so small it's essentially 0

>>8391614
>durr how do I know the right way to solve the problem
Try not being a fucking mouthbreather

>>8391885
so everything divided by infinity is always 0?

>>8391539
Why are you doing precalculate when you clearly have yet to pass middle school algebra?

>>8391893
Any constant divided by infinity yes

>>8391882
As I said, an elementary theorem of limits is that the limit as x approaches infinity of 1/x is 0. If you want to see why this is true then you better get ready for some tough analysis.

But you don't want that so just take it as true. It is a theorem after all.

Limits also have some rules of arithmetic assigned to them, which are also theorems. Particularly

The limit as x approaches anything of

k*f(x) where k is a constant and f(x) is a function of x

Is equal to k * lim(f(x))

So here we can apply these two theorems.

Lim ( 7/x) = Lim (7 * 1/x) = 7*Lim(1/x) = 7*0 = 0

That would be the formal proof of 7/r = 0 when r approaches infinity.

So what should you do now?

READ THE FUCKING THEOREMS GOD DAMN GOOGLE.COM

Mathematicians worked on LONG FUCKING ASS proofs for all these seemingly elementary things... FOR CENTURIES and now they are on the internet there, waiting to be read.

You just have to read it and apply it. As simple as that. Just do it man.

>>8391889
>Try not being a fucking mouthbreather

Isnt it a shame that most math people barely explain better than this?

>>8391866
Wow, how fucking surprising that your algebraic topo prof doesn't have time to explain fields to you!

>>8391896
Because its required?

>>8391903
/thread

You don't properly understand something unless you can explain it to a layman. That or you're being a huge mongoloid for bothering to post without some sort of explanation.

OP, just drop out and save yourself the time, energy, and money

>>8391950
I don't want to be unemployed.