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The Hanging Monkey wrote:Well yes, "d" indicates a small change, but I don't see how small changes are relevant to working out a general relationship.
Other than that I followed the mathematics CarlPierce posted fairly easily.
Darkchilde wrote:The Hanging Monkey wrote:Well yes, "d" indicates a small change, but I don't see how small changes are relevant to working out a general relationship.
Other than that I followed the mathematics CarlPierce posted fairly easily.
Exactly why I have not taken that route. It requires a lot more explanation and requires understanding the concept of a limit.
The Hanging Monkey wrote:Well yes, "d" indicates a small change, but I don't see how small changes are relevant to working out a general relationship.
Other than that I followed the mathematics CarlPierce posted fairly easily.
CarlPierce wrote:You use the small change idea to find the gradient at a particular point.
CarlPierce wrote:The idea being that the smaller and smaller the change is the better and better the answer is
The Hanging Monkey wrote:CarlPierce wrote:You use the small change idea to find the gradient at a particular point.
And the gradient at any point will give you the general rule?CarlPierce wrote:The idea being that the smaller and smaller the change is the better and better the answer is
You mean as dx tends towards zero, then ignoring the dx^2 term becomes a better approximation, giving a more accurate answer?
I think I have it
My maths is by no means bad, but it is very piecemeal. I haven't studied maths formally since I was 16 but I've picked up bits here and there throughout my degree and Ph.D. It's very satisfying to have some of the many gaps filled in.
Scarlett and Ironclad wrote:Campermon,...a middle aged, middle class, Guardian reading, dad of four, knackered hippy, woolly jumper wearing wino and science teacher.
campermon wrote:Just a thought. When you come to differentiating sines and cosines, would it make sense to introduce the series of these terms to show why we get the result?
e.g. sinx=x+x^3/3!+x^5/5!.... so when differentiated we get 1+x^/2!+x^4/4! etc... (which is cosx).
Scarlett and Ironclad wrote:Campermon,...a middle aged, middle class, Guardian reading, dad of four, knackered hippy, woolly jumper wearing wino and science teacher.
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