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Home Real and Hyperreal Numbers Standard Parts Examples Example 1
 
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Example 1

When Δx is an infinitesimal and x is real, compute the standard part of

3x2 + 3x Δx + (Δx)2.

Using the rules in Theorem 3, we can write

st(3x2 + 3x Δx + (Δx)2) =

=st(3x2) + st(3x Δx) + st((Δx)2) =

= 3x2 + st(3x) · st(Δx) + st(Δx)2 =

= 3x2 + 3x · 0 + 02 = 3x2.
Home Real and Hyperreal Numbers Standard Parts Examples Example 1

Last Update: 2010-11-25