Show it using our denition of ln(x) as intergral between 1 and x of 1/t dt. do not use any other defination. and how could you draw a diagram of this
Why did you not say that in the first place.
Let $\displaystyle x>0$ and $\displaystyle \ln (x) = \int_1^x {\frac{1}{t}dt} $
Now clearly $\displaystyle \frac{d\ln(x)}{dx}=\frac{1}{x}.$
Use the mean value theorem to prove the Napier inequality.
what do you mean by uthe sing mean value theorem to prove the Napier inequality?
Do you know what the mean value theorem says?
You posted this in the analysis forum.
Therefore, we can safely assume that something as basic as that theorem can be used. If not, what level is this question on?