Is the infinitesimal approach good. I have heard of an infinitesimal approach to calculus. Is it better than the normal approach or is it the other way around.
 A: The approach with infinitesimals is equivalent to the one without infinitesimals. Anything you can prove using one formalism, you can prove in the other formalism. The difference is thus cosmetic, and a matter of taste and preference. That is largely influenced by what is historically more common-place, which of course is the infinitesimal-free approach. Whether or not this will remain the situation is hard to predict (if forced, I will bet against infinitesimals). 
There is a trade-off. The infinitesimal-free approach does not require any sophisticated machinery to get going. Taking any definition of the reals one wishes, one can start doing analysis immediately with the $\epsilon - \delta$ definition. However, the arguments take some time to get used to, and they are not particularly a direct translation of one's geometric intuitions into a formal system. The infinitesimal approach (no matter which one) requires some considerable amount of preparatory work (either in the form of logic, or some detailed discussion of axioms which are unfamiliar). There are numerous texts that attempt to ease the reader into the world of infinitesimals. As far as I know, they all present an initial hurdle that is not trivial to get around before one can start doing analysis, though once one is past that hurdle, the arguments are nicer and closer to one's intuition. 
So, if you want to learn analysis, it's probably a good idea to do it the infinitesimal-free way. This is by far the standard language analysts use. If you want to broaden your horizons and learn some more formalisms and deepen your foundations of the subject, spending some time with infinitesimals is a good idea. Also, if you want to impress people in the pub knowing your infinitesimals is a good idea (and also to quickly point at silly fallacies people at the pub say about infinitesimals, you might wish to properly learn the basics). 
