Tagged Questions
2
votes
0answers
28 views
Exponent p-value generated in Excel
Excel gave me a p-value of 1.44909E-09
Notice is does not say .09 but 09
This is confusing me, I am trying to analyze my data but am stuck at this point.
If it were E-9 it could be ...
3
votes
1answer
44 views
Why is real exponentiation continuous in the base?
I know that real exponentiation is continuous in the exponent ($f(x)=a^x$ is continuous), but how do we know real exponentation is continuous in the base?
What I mean is, if $r$ is an arbitrary real ...
0
votes
1answer
82 views
For what $ \alpha \in \mathbb R$ is $ |x|^\alpha $ differentiable in $x=0$?
I came across the following question:
For what $ \alpha \in \mathbb R$ is $ |x|^\alpha $ differentiable in $x=0$?
What I have tried:
Since for $ \alpha = 1 $ is clearly non-differentiable in ...
14
votes
1answer
551 views
Infinite tetration, convergence radius
I got this problem from my teacher as a optional challenge. I am open about this being a given problem, however it is not homework.
The problem is stated as follows. Assume we have an infinite ...
12
votes
6answers
811 views
Proving the inequality $e^{-2x}\leq 1-x$
How do I prove the inequality $e^{-2x}\leq1-x$ for $0\leq x\leq1/2$?
5
votes
2answers
184 views
Slope definition of $e$
A common definition of $e$ is given as
$$e = \lim_{n\rightarrow\infty}\left(1+\frac{1}{n}\right)^{n}$$
which can be proven to be equivalent to
$$e=\lim_{h\rightarrow 0}\ ...
4
votes
3answers
261 views
Proof of exponential from homomorphism property
I am going back through a bunch of calculus I learned in high school and proving the stuff that they just told us was true. Along the way, I found I had to prove that if $f(x+y)=f(x)f(y)$ then $f$ is ...
1
vote
1answer
82 views
Simple estimation $e^{a\sqrt{r}} > r$
I want to prove a simple theorem about contour integration via residues and I need the following estimation:
$e^{a\sqrt{r}} > r$ for any real a > 0 and r >> 0.
Is this true? If so, what is an ...
