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Calculus
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11 Jun 2020

HOW DO YOU SEE IT? The figure shows a region R bounded by a piecewise smooth simple closed path C.

(a) Is R simply connected? Explain.

(b) Explain why , where f and g are differentiable functions.

Chapter 15.4, Problem 44E, HOW DO YOU SEE IT? The figure shows a region R bounded by a piecewise smooth simple closed path C.

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Joram Guingguing
Joram GuingguingLv10
20 Aug 2020

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Related questions

Proof Let , where M and N have continuous first partial derivatives in a simply connected region R. Prove that if C is simple, smooth, and closed, and then .

Proof In Exercises 51 and 52, prove the identity, where R is a simply connected region with piecewise smooth boundary C. Assume that the required partial derivatives of the scalar functions f and g are continuous. The expressions and are the derivatives in the direction of the outward normal vector N of C and are defined by and .

Green’s second identity:

(Hint: Use Green’s first identity from Exercise 51 twice.)

Proof In Exercises 51 and 52, prove the identity, where R is a simply connected region with piecewise smooth boundary C. Assume that the required partial derivatives of the scalar functions f and g are continuous. The expressions

g are the derivatives in the direction of the outward normal vector N of C and are defined by

Green’s first identity:

[Hint: Use the second alternative form of Green’s Theorem and the property div

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