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Re: ATTN: sdfgw

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DragonOfTime is not online. DragonOfTime
Joined: 16 Jul 2008
Total Posts: 56933
01 Oct 2011 07:56 AM
How do I calculus?
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sdfgw is not online. sdfgw
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01 Oct 2011 07:56 AM
is this a genuine question

because i don't know whether to actually explain or just post a whole load of lulzworthy crap
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DragonOfTime is not online. DragonOfTime
Joined: 16 Jul 2008
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01 Oct 2011 07:58 AM
Both at the same time

I want to calculus because I can't take going over quadratic equations for the 5 billionth time in maths
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sdfgw is not online. sdfgw
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01 Oct 2011 07:58 AM
ok

lemme through this at you

what is the gradient of y = 3x + 6

if that's easy then

what is the gradient of y = x^2

think about it
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DragonOfTime is not online. DragonOfTime
Joined: 16 Jul 2008
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01 Oct 2011 08:02 AM
Well, the gradient of y = 3x + 6 is going to be 3 unless i am being derp as usual

I know y = x^2 would form a curved line but I have no idea what that would make the gradient
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sdfgw is not online. sdfgw
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01 Oct 2011 08:06 AM
yus

of course you're stumped with x^2 because it's curved, and the gradient changes

the closest thing you can get is the gradient between two points

like

draw a line between two points close to each other on the line, then calculate the gradient of that

the first coordinate would be (x, x^2)

the second would be a certain distance leftwards - we'll say 'h' units away so it would be (x+h, (x+h)^2)

you have to work out the gradient of the line between two points

i'll stop here because it's really confusing and i just want to see your reaction so far
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HiGuiseItsChaos8 is not online. HiGuiseItsChaos8
Joined: 01 Jun 2011
Total Posts: 798
01 Oct 2011 08:07 AM
omg

So gradient is the european equivalent of the slope?

because here in the US we call it the slope


im going to start calling it the gradient
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HiGuiseItsChaos8 is not online. HiGuiseItsChaos8
Joined: 01 Jun 2011
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01 Oct 2011 08:08 AM
oh wait

the gradient is a vector isnt it
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sdfgw is not online. sdfgw
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01 Oct 2011 08:08 AM
yh I actually found out that it's called 'slope' in america a few weeks ago

before I thought everyone called it gradient but then

slope

I mean

GET SOME CLASS
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sdfgw is not online. sdfgw
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01 Oct 2011 08:09 AM
@Hi:

nup, just a number

gradient = change in y / change in x

no length
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HiGuiseItsChaos8 is not online. HiGuiseItsChaos8
Joined: 01 Jun 2011
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01 Oct 2011 08:09 AM
"I mean

GET SOME CLASS"

i know right

it's stupid :(
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DragonOfTime is not online. DragonOfTime
Joined: 16 Jul 2008
Total Posts: 56933
01 Oct 2011 08:11 AM
Oh god, I've never been amazing at this

So if x = 5 then co-ordinates would be (5, 25) and then ((5+h), (25+h^2))?

This would be so much easier if I could make a graph
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sdfgw is not online. sdfgw
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01 Oct 2011 08:12 AM
well when i become the universe king of maths

(note: maths)

i'm going to write a law saying that it must always be referred to as "gradient"

also less survey crap and more binomial expansion in statistics GCSE
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zackmartin is not online. zackmartin
Joined: 13 Aug 2007
Total Posts: 2455
01 Oct 2011 08:13 AM
IM IN SEVENTH GRADE AND I DO NOT UNDERSTAND THESE BIG WORDS D:
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DragonOfTime is not online. DragonOfTime
Joined: 16 Jul 2008
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01 Oct 2011 08:14 AM
Oh yeah, also, Denny burnt all me Chekhov books. Sorry.
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sdfgw is not online. sdfgw
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01 Oct 2011 08:15 AM
"So if x = 5 then co-ordinates would be (5, 25) and then ((5+h), (25+h^2))?"

close

first point is right, second one would be (5+h, (5+h)^2)

the formula for gradient of a line between two points is as I said earlier, change in y / change in x

change is x is easy, it's just

5+h - 5 = h

change in y:

(5+h)^2 - 25

= 25 + 10h + h^2 - 25

= 10h + h^2

so the gradient is (10h + h^2) / h = 10 + h

so, at the point (5, 25), the gradient is 10 + however long the line's x is

how much sense did that make because we haven't done this properly algebraically yet
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sdfgw is not online. sdfgw
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01 Oct 2011 08:16 AM
"IM IN SEVENTH GRADE AND I DO NOT UNDERSTAND THESE BIG WORDS D:"

welcome

we're doing calculus
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DragonOfTime is not online. DragonOfTime
Joined: 16 Jul 2008
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01 Oct 2011 08:19 AM
how much sense did that make because we haven't done this properly algebraically yet
_______

I sort of see how you get from one step to the next

Although I'm not entirely sure why the steps are taken
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LurerreIsIdiot is not online. LurerreIsIdiot
Joined: 09 Apr 2010
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01 Oct 2011 08:24 AM
How the hell the girl can maths?
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DragonOfTime is not online. DragonOfTime
Joined: 16 Jul 2008
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01 Oct 2011 08:24 AM
How the hell the girl can maths?
_______

I can't maths though. That's the point.
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sdfgw is not online. sdfgw
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01 Oct 2011 08:25 AM
excellent

the goal is to make an expression for the gradient at any point

before we used 5 - now let's assume we don't know the point, so we use x

point 1: (x, x^2)
point 2: (x+h, (x+h)^2)

change in x = always h. convenient, right

change in y = (x+h)^2 - x^2
= x^2 + 2hx + h^2 - x^2
= 2hx + h^2

gradient = 2x + h

now if you can visualise it, the closer the two points, the more accurate the gradient

so if the two points were exactly the same, then the gradient would be exact

and if the two points were the same, h would equal zero

so

the gradient of any point on the line y = x^2 is 2x

fascinating

anyway, that's the basics of the first branch of calculus. 's called differentiation, used to find the gradient of any polynomial

the other branch is called integration, and it's pretty much the exact opposite
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DragonOfTime is not online. DragonOfTime
Joined: 16 Jul 2008
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01 Oct 2011 08:30 AM
and if the two points were the same, h would equal zero
_______

Obviously.

And I understand, now.
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sdfgw is not online. sdfgw
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01 Oct 2011 08:33 AM
that's pretty impressive then

though strictly speaking h isn't 0, it's just 1/infinity, but I skimmed over the concept of limits

the notation for a derivative equation (e.g. y = x^2) is:

dy/dx = 2x

the notation for a derivative function (e.g. f(x) = x^2) is:

f'(x) = 2x

also it'd be exceptionally hard to prove it to you but:

y = x^2
-> dy/dx = 2x

y = x^3
-> dy/dx = 3x^2

y = x^4
-> dy/dx = 4x^3

y = x^5
-> dy/dx = 5x^4

y = x^6
-> dy/dx = 6x^5

PATTURN
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