Chapter 15.1, Problem 52E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

(a) In what way are the theorems of Fubini and Clairaut similar?

(b) If *f*(*x, y*) is continuous on [*a*, *b*] × [*c*, *d*] and
*a < x < b*, *c < y < d,* show that *g _{xy}* =

**(a)**

To determine

**To explain:** The similarity of the Fubini and Clairaut theorems.

Explanation

**Theorems used:**

**Clairaut’s theorem:**

Suppose *f* is a real-valued function of two variables *x,y* and
*U* of
*U*. Then,
*U.*

**Fubini’s theorem:**

If *f* is continuous on the rectangular region,

**(b)**

To determine

**To show:**

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