Defining Simplest Function with Specific limit superior

[tortoise]

Ahoy,

It's been four years since I've done any calculus, but I'm working on a project that involves creating a nonlinear equation or a set of equations that will simulate empirical findings based on a specific cognitive theory. I was doing fine but I'm stumped on limits. The function increases by n+1 but I need it to conform to a specific upper limit (which is defined by another equation, but lets use 10 for example).

So my question is how do I go about creating a function with an upper limit of 10, so that as x->infinity, f(x)->10 ?
I understand the concept of limits, and I've figured out how to create a limit at 0 for another function through example but that's where my knowledge ends.

If I had time to start from the ground up I would but I unfortunately don't.

Any help is appreciated.

Cheers

 

[galactus]

If I am understanding correctly, \(\displaystyle \lim_{x\to \infty}\left[\frac{1}{x}+10\right]\)

should work. It's a function and the limit is certainly 10 as \(\displaystyle x\to \infty\)

 

[chrisr]

Something like 10(1-e[sup:38p1h97o]-x/8[/sup:38p1h97o]) or simply 10(1-e[sup:38p1h97o]-x[/sup:38p1h97o]) would have 10 as an upper limit.

 

[BigGlenntheHeavy]

\(\displaystyle Let \ f(x) \ = \ 10.\)

\(\displaystyle \lim_{x\to\infty}f(x) \ = \ 10.\)

\(\displaystyle Can't \ get \ any \ simpler.\)

 

[chrisr]

If you have a non-linear function tending to zero, above the x-axis.
If you now change it's sign, from positive to negative, it will be approaching zero from below the x-axis.
If you add 10 to this function, it will be approaching 10 from below,
so 10 will be it's upper limit.

That's one way to find a non-linear function approaching 10 as the variable tends to infinity,
while rearranging what you already achieved.