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University of Florence


Nov
25
answered Possible Intersection of Intervals
Nov
25
comment Could someone explain the Lagrangian Method?
the tangent to the constraint $g=0$
Nov
23
answered Could someone explain the Lagrangian Method?
Nov
23
answered Formula of regular 2m-gon inscribed in a unit cirlce
Nov
23
revised How can I find the example of $f(x)$ such that $\,\lim_{x\to\infty}f(x) \neq 0$?
deleted 70 characters in body
Nov
23
answered How can I find the example of $f(x)$ such that $\,\lim_{x\to\infty}f(x) \neq 0$?
Nov
22
answered What is the difference between convergence of a sequence and convergence of a series?
Nov
20
answered Proof $x=\sin(x+1)$ has one solution in $\mathbb{R}$
Nov
18
comment Rolling ellipse on line - tangent and normal of roulette
$F$ and $K$ are fixed on the ellipse, so their distance is fixed. At time $t$ it happens that $K(t)$ is on the line, at other times the tangent point will be different.
Nov
18
answered Studying the differentiability of a function at a point $(a_{1},a_{2})$
Nov
18
answered Proving the convergence/divergence of a seemingly oscillating series
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).