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Q. 21

Found in: Page 976


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

In Exercises 21–26, find the discriminant of the given function.


The answer is -4e4x.

See the step by step solution

Step by Step Solution

Step 1. Given Information.

The function is fx,y=e2xcosy.

Step 2. Explanation.

The discriminant is calculated by formula,


Find fx, 2fx2, fy, 2fy2 and localid="1649783903210" 2fxy

fx=2e2xcosy, 2fx2=4e2xcosy

fy=-e2xsiny, localid="1649783850374" 2fy2=-e2xcosy

localid="1649818601411" 2fxy=-2e2xsiny

Step 3. Calculate Discriminant.

Calculate detHf=2fx2·2fy2-2fxy2

localid="1649818688351" detHf=4e2xcosy-e2xcosy--2e2xsiny2 =-4e4xcos2y-4e4xsin2x =-4e4x

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