These identities for $\int_0^1 x^ {-x}\ dx$ and $\int_0^1 x^x\ dx$ are sometimes called the "sophomore's dream". Look that up on Wikipedia.

Apr 20, 2016 · For instance, what if $f (x)$ was actually the function where $x \mapsto x³-4$? Then "$f (x) = x^2$" would be an equation to solve, not a definition of a function.

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Jun 25, 2014 · I have started seeing the "∈" symbol in math. What exactly does it mean? I have tried googling it but google takes the symbol out of the search.

Mar 13, 2018 · My question is: Show that $\lim_ {x \rightarrow c} \frac {x^c-c^x} {x^x-c^c}$ exists and find its value. Because the limit is 0/0 I've tried using L'Hopital's rule, but every time I …

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Any number, when multiplied by 0, gives 0. However, infinity is not a real number. When we write something like $\infty \cdot 0$, this doesn't directly mean anything; rather, it's shorthand for a …

Aug 26, 2014 · I mean, how to solve $e^x=x$ in the complex plane? Is there a solution? I know there is no real solution to this because apparently, $y=x$ and y=$e^x$ have no ...

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In physics, this is usually used as dependent versus independent as in a velocity versus time or position versus time graphs. See Motion graphs and derivatives as well as from Line chart we …