Question

I have a question about growth ranking

Answer 1

So, we are taking about different growths.
From smallest to greatest

1) Polynomials
- linear growth
- quadratic polynomial (with positive coefficient)
- cubic polynomial (with positive coefficient)
- etc... (some nth degree polynomial)

2) Exponential function f(x)=a(b)\(^x\)
- this exponential eventually exceeds the polynomial

3) factorial

4) n\(^n\)

Answer 2

So, would I put hyperbolic functions in the exponential?

what I want to propose is that a hyperbolic function (as lim x→∞) is smaller than or equivalent to e\(^x\), and larger than any other exponential function if the base of this exponential function is less than e.

Answer 3

yes

Answer 4

(and of course is base is bigger than e, this exponential is certainly exceeds hyperbolic)

Answer 5

oh yes? nice

Answer 6

define hyperbolic function

Answer 7

well, it consists of some e^x componenets

Answer 8

cosh(x) for example is the average between e^X AND E^-X

Answer 9

So...

`hyperbolic function` ≥ `(a)^x; where a≤e`
`hyperbolic function` < `(a)^x; where a>e`

Answer 10

if the difference is the base, then yes

Answer 11

yes, with same x exponent... tnx
(I was just thinking of different growths)

Answer 12

you can wolfram alpha it to make sure

Answer 13

test it with one concrete condition where a>e

Answer 14

I started this proposal when I proved that e^x is greater than cosh(x)