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Real Analysis
book

Real Analysis

by V. Karunakaran
May 2024
Intermediate to advanced content levelIntermediate to advanced
585 pages
15h 38m
English
Pearson India
Content preview from Real Analysis
“real: chapter_06” 2011/5/22 23:14 page3—#3
Differentiation 6-3
6.2 DEFINITION OF DERIVATIVE, EXAMPLES AND
ARITHMETIC RULES
Definition 6.2.1 Let S R. Let L(S) denote the set of limit points of
S and x S L(S). We say that f is differentiable at x if
f
(x) = lim
tx
f (t) f (x)
t x
exists as a real number. We also call f
(x) as the derivative of f at x. If
f is differentiable at all points of S, then we say that f is differentiable
on S.
Note 6.2.2 If S is an interval and x is not an end point of S, then t can
approach x with either of the conditions t > x or t < x. This f
(x) will
be called the two-sided derivative of f at x . For similar reasons, ...
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Publisher Resources

ISBN: 9781299447561Publisher Website