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Chapter 14: Q. 17 (page 1119)

If S is parametrized by r(u, v), why is dS=ru脳rvthe correct factor to use to account for distortion of area?

Short Answer

Expert verified

Hence,thecorrectfactortousetoaccountfordistortionofareaisdS=ruandrvdudv

Step by step solution

01

Step 1. Given 

The r(u, v) is parametrized

02

Step 2. Finding area of parallelogram 

Theareaoftheparallelogramwithsidesruandrvis,Thearear,ruandrv,ofthisparallelogramapproximatestheareaoftheportionofthetangentplaneusedtoapproximatetheareaofS;inthelimit,theanalogyisexact.Hence,thecorrectfactortousetoaccountfordistortionofareaisdS=ruandrvdudv

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