ÇáÓáÇã Úáíßã
ÚäÏí ÓæÇá íÇáíÊ Çáí íÞÏÑ Íáå áí æãÔßæÑíä
(ÍÓÇÈ ÇáÊÝÇÖá æÇáÊßÇãá íÊØáÈ)
a) Let n be a positive integer. Show that the relation R
on the set of all polynomials with real-valued coeffi- .
cients consisting of all pairs (f, g) such that I(n)(x) =
g(n) (x ) is an equivalence relation. [Here I(n)(x) is the
nth derivative of I(x).]
b) Which functions are in the same equivalence class as
the function I(x ) = x\ where n = 3 ?
ÇäÊÙÑ ÑÏæÏßã
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