growth of a function

Mark Forums Read

		Physics Forums > Mathematics > General Math
growth of a function

Reply

growth of a function

Thread Tools

Search this Thread

Nov28-09, 07:00 PM	#1
Jarle Jarle is Offline: Posts: 650	growth of a function Does there exist a continuous function which outgrows polynomial growth, but not exponential growth? I.e. does a there exist a continuous function f such that $LaTeX Code: \\frac{x^n}{f(x)} \\to 0$ and $LaTeX Code: \\frac{f(x)}{a^x} \\to 0$ for all positive real n and a?

PhysOrg.com
PhysOrg

PhysOrg

mathematics news on PhysOrg.com

>> Researcher to track spread of disease, malware and power outages
>> Spherical cows help to dump metabolism law: 3/4-power law is actually 2/3
>> Nonlinear thinker: Making sense of previously insoluble problems

Nov28-09, 08:33 PM	#2
hamster143 hamster143 is Offline: Posts: 615 Recognitions: PF Contributor	Re: growth of a function Yes. Look at it this way: you take logs of the polynomial and the exponential, you get $LaTeX Code: g_1(x) = C_1 \\ln x$ and . Can you find a function that grows faster than g_1 and slower than g_2 for all C? Clearly you can, because ln grows extremely slowly.

Nov28-09, 10:09 PM	#3
Jarle Jarle is Offline: Posts: 650	Re: growth of a function Thanks, $LaTeX Code: x^{\\sqrt{x}}$ is such a function.

Nov28-09, 11:03 PM	#4
hamster143 hamster143 is Offline: Posts: 615 Recognitions: PF Contributor	Re: growth of a function Or $LaTeX Code: e^{\\sqrt{x}}$ , or $LaTeX Code: e^{x/\\ln{x}}$ .

Nov29-09, 09:31 AM	#5
Jarle Jarle is Offline: Posts: 650	Re: growth of a function I'm sure we can find many as you pointed out.

Reply

Thread Tools
Show Printable Version Email this Page

Similar Threads for: growth of a function
Thread	Thread Starter	Forum	Replies	Last Post
DE equation modeling growth off a tan function	Outlaw747	Calculus & Beyond	2	Jan26-09 11:59 AM
General question about growth function?	cango91	Calculus & Analysis	1	Dec9-08 08:43 AM
Hey, I need help on log and continuous growth.	firstwave	Introductory Physics	1	Oct1-05 06:07 PM
Simple function growth	ti89fr33k	Calculus & Analysis	9	Mar28-05 08:49 PM
Function Growth Rates	Klion	Introductory Physics	7	Sep29-04 02:03 AM