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Calculus: Differentiation and Integration, 1st Edition
book

Calculus: Differentiation and Integration, 1st Edition

by ICFAI
April 2024
Intermediate to advanced content levelIntermediate to advanced
710 pages
20h 50m
English
Pearson India
Content preview from Calculus: Differentiation and Integration, 1st Edition
Real Numbers 1-11
x x y y
x y y
x y x y
= +
+
(by Triangle Inequality)
, which is thhe required result.
m.
x y x y x y+ = + iff 0
Proof directly follows from the definition.
n.
x y x y x y = iff 0
Proof directly follows from the definition
o.
1
2
[ ] max{ , }x y x y x y+ + =
Proof:
Consider
x y x y x y x y x y e
x y x
+ + = + +
= + +
max{( ), ( )} ( )
max{ (
by property
yy x y x y
x y x y x y x y
x y
x y
), ( )}
max{ , }
max{ , }
max{ ,
+
= + + + +
=
=
2 2
2
}}
max{ , }Hence, x y x y x y+ + = 2
And this leads to the desired result,
1
2
x y x y x y+ +
= max{ , }
Similarly, we can prove the following result.
1
2
x y x y x
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Publisher Resources

ISBN: 9789353948221