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Prove that $\forall x > 0, x - 1 \ge \ln(x)$
Prove that $\forall x > 0, x - 1 \ge \ln(x)$ .
Here is my proof:
We prove the inequality on two intervals, $(0,1]$ and $[1,+\infty)$.
First the easier one, $[1,+\infty)$.
Notice that at $x=1$, ...
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Proving or disproving: If $0<a<b<1$, then $(1-a)^b>(1-b)^a$
Prove or disprove
If $0<a<b<1$, then $$(1-a)^b>(1-b)^a$$
I think this looks true when evaluating the differential equation $\frac{dy}{dx}=-y$ with initial condition $y(0)=1$ using euler ...
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