Expanding this by the binomial theorem (see p. 141), we get
|
.
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So, neglecting the small quantities of higher orders of smallness, we have:
.
Subtracting the original , we find
- ,
- .
And this is still in accordance with the rule inferred above.
Case of a fractional power.
Let . Then, as before,
terms with higher powers of .
Subtracting the original , and neglecting higher powers we have left:
,
and . Agreeing with the general rule.