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Now let us examine the function

We know it is defined for at least one value of* x*, and it is quite easy to see that it will also converge to a number between 1 and *e* for *x *between 0 and 1.

We can virtually copy-paste the binomial expansion from the previous page to get

this will give us

And in the same way as in the previous page, we will get

Next, what happens if we take the derivative of this function? We get

I.e., the same function as we started with.

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