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idku
 one year ago
I have a question about growth ranking
idku
 one year ago
I have a question about growth ranking

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idku
 one year ago
Best ResponseYou've already chosen the best response.0So, 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\(^n\)

idku
 one year ago
Best ResponseYou've already chosen the best response.0So, 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.

idku
 one year ago
Best ResponseYou've already chosen the best response.0(and of course is base is bigger than e, this exponential is certainly exceeds hyperbolic)

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1define hyperbolic function

idku
 one year ago
Best ResponseYou've already chosen the best response.0well, it consists of some e^x componenets

idku
 one year ago
Best ResponseYou've already chosen the best response.0cosh(x) for example is the average between e^X AND E^X

idku
 one year ago
Best ResponseYou've already chosen the best response.0So... `hyperbolic function` ≥ `(a)^x; where a≤e` `hyperbolic function` < `(a)^x; where a>e`

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1if the difference is the base, then yes

idku
 one year ago
Best ResponseYou've already chosen the best response.0yes, with same x exponent... tnx (I was just thinking of different growths)

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1you can wolfram alpha it to make sure

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1test it with one concrete condition where a>e

idku
 one year ago
Best ResponseYou've already chosen the best response.0I started this proposal when I proved that e^x is greater than cosh(x)

idku
 one year ago
Best ResponseYou've already chosen the best response.0then sinh(x) is certainly smaller

idku
 one year ago
Best ResponseYou've already chosen the best response.0e^x is always >0 e^x is always <0 :)

idku
 one year ago
Best ResponseYou've already chosen the best response.0e^x is always >0, (correction). but that is always >0 as well.

idku
 one year ago
Best ResponseYou've already chosen the best response.0other functions are also obviously less than e^x.

idku
 one year ago
Best ResponseYou've already chosen the best response.0So I want to change my statment a bit

idku
 one year ago
Best ResponseYou've already chosen the best response.0`hyperbolic function` < `(a)^x; where a≥e ` `hyperbolic function` > `(a)^x; where a<e`
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