Tagged Questions
20
votes
2answers
381 views
How to show that a root of the equation $x (x+1)(x+2) … (x+2009) = c $ can have multiplicity at most 2?
How to show that a root of the equation $$x (x+1)(x+2) ....... (x+2009) = c $$ can have multiplicity at most 2 , and to find the value of $ c $ for which this is possible.
I proceeded by using the ...
1
vote
2answers
94 views
find number of solution for given equation
suppose we we have following equations and conditions
Let $k$ be the number of real solutions of the equation
$e^x+x-2=0$ in the interval $[0, 1]$ and and let $n$ be the number of real solutions ...
1
vote
1answer
38 views
Formula to scale a series that is being bent with a root / power.
I have a reference number, Rx, and a series of numbers, Sx[], to compare to it. Let's call the output Ox[]. I am using a simple square root to accelerate the apparent difference between the reference ...
3
votes
1answer
58 views
Number of roots $|f(|x|)|$ has according to $f$
If $f$ has one root on $(-\infty,0)$ and two distinct roots on
$(0,+\infty)$ and $f(0)=-1$, how many roots does $|f(|x|)|$ have?
I know graph of $|f(|x|)|$ should be in quadrant I because $x$ ...
0
votes
1answer
63 views
First derivative
What would be the further steps for the case like this:
I am finding the first derivative of a function: $f(x) = \ln(1+x^2)$
So the procedure would then be:
$f'(x) = \frac{2x}{1+x^2}$.
$f'(x) ...
2
votes
2answers
226 views
Chord dividing circle , function
Two chords PA and PB divide circle into three parts. The angle PAB is a root of f(x)=0.
Find f(x)
Clearly , PA and PB divides circle into three parts means it divides it into 3 parts of equal areas
...
1
vote
2answers
111 views
Can the inverse of this logit-like transformation be stated analytically?
For $\alpha \geq 0$ the transformation $x \mapsto \log(x) - \alpha \log(1-x)$
maps the unit interval to the real line (in fact for $\alpha = 0$ the transformation is not surjective). For $\alpha=1$ ...
