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University of Florence


Mar
22
reviewed Approve suggested edit on prove that $x'Ax=\mathrm{tr}(xAx')=\mathrm{tr}(Axx')=\mathrm{tr}(xx'A)$
Mar
22
answered Vector valued function: What part of the train is always moving backward?
Mar
21
answered Derivative of an integral variable confusion?
Mar
21
answered Can the chain rule be relaxed to allow one of the functions to not be defined on an open set?
Mar
20
revised What's the intuition behind Pythagoras' theorem?
edited body
Mar
20
comment How to suceed in mathematical olympiads and competitions?
I would add: you could also post here the exercises where you need help.
Mar
20
comment How does the exponent of a function effect the result?
I don't agree... There should be no confusion on which is the order of operations in $(-1)^{\frac 2 2}$. The problem is that the rule $x^{\frac a b} = (x^a)^{\frac 1 b}$ is so strong in our mind, that we don't notice that actually we should first compute the fracion $\frac a b$ and then the power.
Mar
20
comment Find equation of tangents to curve
I think so.....
Mar
20
awarded  Nice Answer
Mar
19
revised How does the exponent of a function effect the result?
added 63 characters in body
Mar
19
comment How does the exponent of a function effect the result?
However I find very dangerous (and formally wrong) to introduce a notation where $x^{4/6} \neq x^{2/3}$. What happens if you have $x^a$ with $a=4/6$? You should conclude that $x^a \neq x^{4/6}$.
Mar
19
answered Find equation of tangents to curve
Mar
19
revised How does the exponent of a function effect the result?
added 76 characters in body
Mar
19
comment How does the exponent of a function effect the result?
However you would agree that $(-1)^2$ IS defined... So the conclusion of my first comment.
Mar
19
comment How does the exponent of a function effect the result?
$2/2=1$. So $x^{\frac 2 2}$ and $x^1$ are the same thing.
Mar
19
comment How does the exponent of a function effect the result?
$-1<0$ and $2$ is even. So, you are saying that $(-1)^{\frac 4 2}$ is not defined.
Mar
19
comment How does the exponent of a function effect the result?
So you are saying that $(-1)^{\frac 4 2}$ is not the same as $(-1)^2$?
Mar
19
comment How does the exponent of a function effect the result?
But the OP has asked about $(x^2)^{\frac 1 2}$ with respect to $x^1$ which are both defined for all $x$.
Mar
19
comment How does the exponent of a function effect the result?
What? $x^{\frac 2 2} = |x|$ is horrible...
Mar
19
comment How does the exponent of a function effect the result?
you mean that $(-1)^2$ is not the same as $(-1)^{\frac 4 2}$?