 # "How does exp(x) keep showing up in mathematics When I first learnt about e, I just treated it as another number (as far as I know, it doesn't even have a natural definition), but how is it that exp(x) is so important and keeps showing up at various places in mathematics?" Slovenujozk 2022-09-12 Answered
How does exp(x) keep showing up in mathematics
When I first learnt about e, I just treated it as another number (as far as I know, it doesn't even have a natural definition), but how is it that exp(x) is so important and keeps showing up at various places in mathematics?
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e is very important because it keeps showing up in various places in mathematics. Specifically, calculus though.
Calculus is the study of the rate of change, and the first time you have possibly learned about the number e, you spot how a whole lot it performs a key role within the charge of exchange of bank interest, or exponential boom/decay. given that calculus is the examine of rate of variety, e is certain to appear in many factors across calculus, whether or not that be derivatives, integration, polynomials, many superior topics too like differential equations.

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One beautiful occurrence I just found out today:
Consider the equation:
${x}^{y}={y}^{x}$
$x,y\in {R}^{+}$
For every positive value of x, there are two values of y that satisfy the above equation ONLY after x= e and vice versa.
To admire this amazing result, look at the graph of the equation on Desmos.

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