Wheres's the math?

Cisco Qid

Well-known member
I developed this definition for e, some years back









I know that I was frustrated when they simply gave the answer f'(x) = exp(x) where e = limit as n goes to infinity of (1+1/n)^n. No matter which Calculus book, my question was always, why?
 
Calculate the derivative of some base to the power of x or ax by the following method


(ax)' = f'(x) = Lim (h -> 0) (ax+h - ax)/ h = ax Lim h->0 (ah - 1)/h


In this case, we are interested values of a where: Lim h->0 (ah - 1)/h = 1


or (ah - 1)/h = 1


Solve for a: ah - 1 = h and ah = 1 + h


or a = (1+h)1/h


or a = Lim h->0 (1+h)1/h


Let n = 1/h then n goes to infinity as h goes to zero or:


a = Lim n-> infinity (1 + 1/n)n This is the definition of Euler's constant, e.


Thus if a is equal to Euler's constant e then f(x) = f'(x) = ex where


e = Lim n-> infinity (1 + 1/n)n
 
I developed this definition for e, some years back









I know that I was frustrated when they simply gave the answer f'(x) = exp(x) where e = limit as n goes to infinity of (1+1/n)^n. No matter which Calculus book, my question was always, why?

Why?

Here is an explanation using a continuous interest paradigm:


I'm comfortable with a factorial definition as a series. "It's the natural language of calculus." (Timestamp = 7.00 +...) :cool:
___
 
Last edited:
My math editor doesn't work here.

On the subject of the english of mathematical language, why do British people say "maths" and Americans say "math"? As I understand the term, the word math is either plural or singular depending on the context.

__
 
Last edited:
Back
Top