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University of Florence


Nov
18
answered Rolling ellipse on line - tangent and normal of roulette
Nov
18
comment Rolling ellipse on line - tangent and normal of roulette
$K$ is the center of the "infinitesimal rotation" of the point $F$. So the velocity of $F$ is perpendicular to $FK$.
Nov
17
comment Prove or disprove: functions
Maybe $X'$ is the complementary set of $X$?
Nov
11
revised About Banach Spaces And Absolute Convergence Of Series
typo
Nov
11
comment Limit of derivatives and continuous
$\lim_{x\to 1^-} f'(x) = \lim_{x\to 1^-} \frac{1}{(1-x)^2} = +\infty$, it exists even if it is not finite.
Nov
7
comment Limit of derivatives and continuous
But, again, this is true only if the limit of $f'$ exists and it is finite.
Nov
7
comment Limit of derivatives and continuous
It is possible that the limit of $f$ is infinite and the limit of $f'$ exists. Take $f(x) = 1/(1-x)$.
Nov
7
revised Limit of derivatives and continuous
deleted 1 character in body
Nov
7
comment Limit of derivatives and continuous
It is correct if you take $h(x) = g(1/2) + \int_{1/2}^x g'(t)dt$ (check the sign).
Nov
7
comment Limit of derivatives and continuous
Continuity of a function tells nothing in the points outside the domain.
Nov
7
answered Limit of derivatives and continuous
Nov
7
comment Arithmetic operations on sets
With the notation suggested in my answer below, $\mathbb Z + \mathbb Z = \mathbb Z$, since every integer is the sum of two integers.
Nov
6
answered Arithmetic operations on sets
Nov
6
comment Give an example of an infinite compact set $A$ such that its supremum is not a limit point
Have you been given an example of correct answer?
Nov
6
answered Prove that if $3\mid n^2 $ then $3\mid n $.
Nov
6
comment Prove that if $3\mid n^2 $ then $3\mid n $.
what's your definition of prime number?
Nov
6
comment If $f$ is bounded and twice differentiable in $\mathbb{R}$, show that there exists $\xi\in\mathbb{R}$, s.t. $f''(\xi)=0$.
Lemma 3 is false: take $f(x)=atan(x)$
Nov
6
comment If $f$ is bounded and twice differentiable in $\mathbb{R}$, show that there exists $\xi\in\mathbb{R}$, s.t. $f''(\xi)=0$.
en.wikipedia.org/wiki/Darboux%27s_theorem_%28analysis%29
Nov
6
comment If $f$ is bounded and twice differentiable in $\mathbb{R}$, show that there exists $\xi\in\mathbb{R}$, s.t. $f''(\xi)=0$.
The intermediate value theorem is true for the derivative of a function even if the derivative is not continuous.
Nov
6
revised If $f$ is bounded and twice differentiable in $\mathbb{R}$, show that there exists $\xi\in\mathbb{R}$, s.t. $f''(\xi)=0$.
added 40 characters in body