Tagged Questions
0
votes
0answers
133 views
Approximate a complicated mystery function
Let there exist a mystery function ƒ.
ƒ accepts exactly 2 arguments, A & B.
As B approaches A, ƒ approaches A, at a simple exponential growth rate E.
As B approaches 0, ƒ approaches the mean ...
1
vote
1answer
72 views
0
votes
1answer
80 views
How do I solve this exponential equation?
$$x = 2^{x-3}$$
Does there exist an analytical solution to this equation? If so, how do I find it?
What if it is changed to an equality?
$$x>2^{x-3}$$
30
votes
11answers
2k views
How is $e^x$ read aloud?
My current research colleague from New Castle told me that I was reading it wrong. I usually read it as e power x.
How do you read aloud $e ^ x$?
Is it:
e raised to x
e power x
e powered x
or e ...
3
votes
3answers
210 views
What is the fractional part function of $e^x$?
Given a real positive number $x\in\mathbb{R^+}$.
What is the function of the fractional part of $e^x$?
4
votes
1answer
57 views
Find the absolute maxmium of the function $f(x) = x \cdot {e}^{-x}$
How can I find the absolute maximum of this exponential function?
$f(x) = x \cdot {e}^{-x}$
I know that the first step is to take the derivative of the function, like so:
${f}^{\prime}(x) ...
4
votes
3answers
655 views
Examples of continuous growth rates greater than exponential
I read on Wikipedia that growth rate of a function can sometimes be greater than exponential. Can you give me some examples of such functions (preferably continuous ones)?
Obviously $x^x$ grows ...
1
vote
2answers
276 views
Fixed points of $e^z$
How would one find the fixed points of $e^z$, where $z$ is complex (if there are any)? I feel this problem probably has a really obvious answer, and for some reason, I'm just not getting it. Thanks.
4
votes
3answers
409 views
How to find a Newton-like approximation for that function?
I want to find the complex fixpoint $t=b^t $ for real bases $b> \eta = \exp(\exp(-1))$.
added remark: I'm aware that there is a solution using branches of the Lambert-W-function, but I've no ...
