22 August 2019
Losing it on a tangent
Osserviamo Osserviamo alcune identità...
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mathematical dialogues
26 July 2019
Feeling grilled?
Get pen and paper and draw a cartesian plane. Then draw, on it, a set of points with integer coordinates, such as \(A(1,1)\), \(B(1,0)\), \(C(2,0)\), \(D(3,2)\), and so forth......
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10 July 2019
The bare necessities
This is the first of a series of posts in which a problem is presented to the reader, who in invited to solve it by following a proposed path. The background knowledge required...
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9 July 2019
Rock and rolle
Continuing were we left on a previous post about non differentiable functions that however have a well defined right derivative, we want now to show that...
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6 July 2019
Ups and downs
We are given a function \(f(x)\), for which the right derivative
\[f'_+(x) = \lim_{h\rightarrow 0^+}\frac{f(x+h)-f(x)}{h}\]
is defined in \(\Bbb R\). We also know...
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4 July 2019
Should you be hesitant, value the discriminant
The problem, presented in a previous post, of determining the point on a circumference that is closest to a given interior point \(P\), changes radically if we consider an...
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3 July 2019
If you fear your lack of ability, use triangular inequality
Consider a circle and a point \(P\) inside it. We know that the minimum distance between \(P\) and the points on the circumference is \(2\) cm, while the maximum distance is...
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9 June 2019
Monotonically speaking
The concepts of monotonicity and continuity are very different. However, if we consider a monotonic function whose domain is an interval, we can deduce that right and left limits...
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