# Tagged Questions

316 views

### Approximating Logs and Antilogs by hand

I have read through questions like Calculate logarithms by hand and and a section of the Feynman Lecture series which talks about calculation of logarithms. I have recognized neither of them useful ...
136 views

### Showing (1 - polynomial fraction) raised to a polynomial power is a negligible function

Let $P(k)$ and $Q(k)$ be two polynomials ($k>0$). Let $\mathrm{neg}(k)$ be a negligible function for sufficiently large $k$ (see Appendix on question for definition). Does someone know how to show ...
205 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 ...
106 views

### Approximation with 1-exponential

How come that $$\left(1-\frac{1}{x}\right)^x \approx e^{-1}\ ?$$ Is there a proof or something to understand this?
213 views

### Approximate solution for an exponential equation

Trying to solve this question: Probability of ball ownership I got at an expression for the solution, P: $$\frac{P}{M} = (1 - \frac{1}{M+N})^{N(1-\frac{P}{M})+M}$$ Where M, N are parameters. The ...
81 views

### Numerically estimate $a^b$ [duplicate]

Possible Duplicate: How can I calculate non-integer exponents? What is the most efficient way to estimate $a^b$ ($a > 0$) numerically? My goal is not to use built-in math functions (like ...
3k views

### Approximation of $e^{-x}$

Is there a method to mentally evaluate $e^{-x}$ for $x>0$? Just to have an idea when computing probabilities or anything that is an exponential function of some parameters.
2k views

### How can I calculate non-integer exponents?

I can calculate the result of $x^y$ provided that $y \in\mathbb{N}, x \neq 0$ using a simple recursive function:  f(x,y) = \begin {cases} 1 & y = 0 \\ (x)f(x, y-1) & y > 0 \end ...
5k views

### How to calculate $e^x$ with a standard calculator

Is there a simple method for calculating the $e^x$ ($x\in\mathbb{R}$) with a basic add/subtract/multiply/divide calculator that converges in reasonable time, preferably without having to memorize ...
512 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 ...