Re: how come calculus can be exact?

From: Phil Holman (philjud_at_earthlink.not)
Date: 09/05/04 

Date: Sun, 05 Sep 2004 18:44:00 GMT

"ashok" <arjdombivli@indiatimes.com> wrote in message
news:1dc813f.0409051006.f35afef@posting.google.com...
> How come calculus gives the exact results despite we are making
> approximations(neglecting the infinitesimal which tends to zero) at
> its basic definition level?
>
> I am getting very much frustated over it.
> Can someone please convince me over the exclusion of the infinitesimal
> terms from the definition and still getting the correct results.??

You really need to study limits. For differentiation, an approximation
based on a small value h becomes an exact solution when h tends to zero.
You can substitute in actual values of .001 and smaller to see how the
solution approaches the exact value. Ex. for y = x^2, calculate dy buy
using x = 1 and x = 1.001. From this calculate dy/dx as .002001/.001 =
2.001. As you decrease the difference to say x = 1 and x = 1.0001, the
closer you get to the exact answer of 2.

PH

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