Recent content by foobar99

Think of it as rate of change of one thing w.r.t another. So, if I get paid P=$2 per foot of ditch, and I dig S=3 feet per day, ##dP/dt = 2, dS/dP = 3##, and ##dP/dt = 6## (i.e., $6 per day). The last one, by the way, is the chain rule. So, loosely speaking, ##dP/dP = 1## - i.e., I get one...

It is a bit of a didactic distinction without foundation, maybe tied to history. Typically, intro calc is divided into differential calc then integral calc. Differential involves only derivatives, built up on the ##\lim \frac{f(x+h)-f(x)}{h}## as h goes to zero. this is slope identification...

I think you may be a bit unclear on the Taylor series itself and how it is being used. The Taylor series gives an approximation to a function f(x) at any point x. It basically gives a way to model the function in a neighborhood of x (imagine x = a) by saying it is the sum of f(a) plus f'(a) x...