The Volumes Experience (1 Viewer)

[maths > english]

my maths tutor said its ok to use the dv = 2πx . f(x) . dx method but u should draw a cyclinder and write:

radius = ...
height = ...
width = ...

just to be sure u get all available marks

going from first principals for each specific question in an exam is very time consuming and should be avoided, if u want to go from first principals u should use a generic proof:

e.g. a "sandwich" limit

anulus area x smaller height < change in volume < anulus area x greater height

π[(x+Δx)²-x²] . f(x) < ΔV < π[(x+Δx)²-x²] . f(x+Δx)

π[2x + Δx] . f(x) < ^ΔV/_Δx < π[2x + Δx] . f(x+Δx)

as Δx → 0, ^ΔV/_Δx → 2πx . f(x)

ΔV → 2πx . f(x) . Δx

[note: inequality signs change for a decreasing function]

 

[Dumsum]

My teacher taught our class to use the formula, but because I taught myself volumes and my textbook does first principles that's just what I'm used to and what I'll be using in the exam.

 

[who_loves_maths]

Originally Posted by Dumsum
My teacher taught our class to use the formula, but because I taught myself volumes and my textbook does first principles that's just what I'm used to and what I'll be using in the exam.

so you're implying that your teacher does NOT teach from first principles??? if that's the case, then obviously he/she is not a good educator.

 

[who_loves_maths]

Originally Posted by maths > english
...
ΔV → 2πx . f(x) . Δx
...

how do you type 'delta': Δ ?

 

[KFunk]

You use an ampersand, followed by Delta, followed by a semicolon.

&_Delta_; = &Delta; (but with the underscores deleted)

Using a lower case d gives you a lower case delta. It works for most of the greek characters:

&Alpha; &alpha; &Beta; &beta; &Gamma; &gamma; &Delta; &delta; etc...

 

[KFunk]

Theres lots of ways, first of all you could use character map.

Or HTML which has too ways. either &(Name); or &#(Number);

http://www.webreference.com/html/reference/character/symbols.html

The useful list to remember (at least partially) would probably be (case sensitive, especially for the greek letters):
pi (&pi; ), theta (&theta; ), fnof (&fnof; ), sum (&sum; ), radic (&radic; ), infin (&infin; ), ang (&ang; ), int (&int; ), there4 (&there4; ), ne (&ne; ), equiv (&equiv; ), le (&le; ), ge (&ge; ), perp (&perp; ), plusmn (&plusmn; ), deg (&deg; )

Xayma's post from the Notation sticky thread is a pretty good reference point for notation in the math forums. [unfortunately it doesn't work in most other places, e.g. physics]

 

[who_loves_maths]

^ ah, okay, thanks KFunk.

 

[maths > english]

My teacher taught our class to use the formula, but because I taught myself volumes and my textbook does first principles that's just what I'm used to and what I'll be using in the exam.

i think its ok to use formulas but u should always make sure u completely understand how it works and how it is derived

in 4u u get rewarded for understanding how things work but unfortunately alot of teachers at bad schools are extremely lazy and try to teach the course through formula memorising

in my school my teacher was lazy and incompetent so i didnt go to class and taught myself the course, those who went to his classes were severely penalised

 

[FinalFantasy]

i think its ok to use formulas but u should always make sure u completely understand how it works and how it is derived

in 4u u get rewarded for understanding how things work but unfortunately alot of teachers at bad schools are extremely lazy and try to teach the course through formula memorising

in my school my teacher was lazy and incompetent so i didnt go to class and taught myself the course, those who went to his classes were severely penalised

hahaha
our 3unit teacher, grabs the text book, and READS it in front of the class and makes everyone else follow
it's like a reading lesson
after the reading session she claims to have taught the topic already LoL

 

[Dumsum]

so you're implying that your teacher does NOT teach from first principles??? if that's the case, then obviously he/she is not a good educator.

Oh he didn't teach the formula straight away, he showed where it came from - once. then he said "just use this formula from now on". Meh, I feel safer doing it from first principles each time.

 

[richz]

dont use it because u get marks for delta V and also the limit