Here is a page for explanations of some of the more tricky questions that turn up occasionally.


Why is $\frac{d}{dx}ln(x)=\frac{1}{x}$ ?

To start with, it's worth looking at the graph and seeing that this is reasonable.

So it seems plausible. How about an exact calculation?

We start with $y=ln(x)$ and we want to compute $\frac{dy}{dx}$

Now the really tricky part is that when y is a one-to-one function of x, which it is in this case if we restrict ourselves to positive x, then $\frac{dx}{dy}=1/\frac{dy}{dx}.$ To see that properly you can either use graphs and swap the co-ordinates around, or you can do the limiting process for each side.

Once you accept that, we have


What is 0.999999... actually equal to?

This is a good one. Students seem to think that it can't be one, because it's "obviously" less than one.

How do you convince them otherwise?


What is the value of $0^0$ ??

Hmm ...

Are there any others?


CategoryMaths
Last change to this page
Full Page history
Links to this page
Edit this page
  (with sufficient authority)
Change password
Recent changes
All pages
Search