Q. 21 In Exercises 21鈥�26, find the d... [FREE SOLUTION]

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Chapter 12: Q. 21 (page 976)

In Exercises 21鈥�26, find the discriminant of the given function.
$f (x, y) = e^{2 x} \cos y$ .

Short Answer

Expert verified

The answer is $- 4 e^{4 x}$ .

Step by step solution

Step 1. Given Information.

The function is $f (x, y) = e^{2 x} \cos y$ .

Step 2. Explanation.

The discriminant is calculated by formula,

$d e t (H_{f}) = \frac{{鈭�}^{2} f}{鈭� x^{2}} 路 \frac{{鈭�}^{2} f}{鈭� y^{2}} - {(\frac{{鈭�}^{2} f}{鈭� x 鈭� y})}^{2}$

Find $\frac{鈭� f}{鈭� x}$ , $\frac{{鈭�}^{2} f}{鈭� x^{2}}$ , $\frac{鈭� f}{鈭� y}$ , $\frac{{鈭�}^{2} f}{鈭� y^{2}}$ andlocalid="1649783903210" $\frac{{鈭�}^{2} f}{鈭� x 鈭� y}$

$\frac{鈭� f}{鈭� x} = 2 e^{2 x} \cos y$ , $\frac{{鈭�}^{2} f}{鈭� x^{2}} = 4 e^{2 x} \cos y$

$\frac{鈭� f}{鈭� y} = - e^{2 x} \sin y$ , localid="1649783850374" $\frac{{鈭�}^{2} f}{鈭� y^{2}} = - e^{2 x} \cos y$

localid="1649818601411" $\frac{{鈭�}^{2} f}{鈭� x 鈭� y} = - 2 e^{2 x} \sin y$

Step 3. Calculate Discriminant.

Calculate $d e t (H_{f}) = \frac{{鈭�}^{2} f}{鈭� x^{2}} 路 \frac{{鈭�}^{2} f}{鈭� y^{2}} - {(\frac{{鈭�}^{2} f}{鈭� x 鈭� y})}^{2}$

localid="1649818688351" $d e t (H_{f}) = (4 e^{2 x} \cos y) (- e^{2 x} \cos y) - {(- 2 e^{2 x} \sin y)}^{2} = - 4 e^{4 x} \cos^{2} y - 4 e^{4 x} \sin^{2} x = - 4 e^{4 x}$

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91影视

In Exercises 21鈥�26, find the discriminant of the given function.
$f (x, y) = e^{2 x} \cos y$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Calculate Discriminant.

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91影视

In Exercises 21鈥�26, find the discriminant of the given function.fx,y=e2xcosy.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Calculate Discriminant.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Decision Maths

Probability and Statistics

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Exercises 21鈥�26, find the discriminant of the given function.
$f (x, y) = e^{2 x} \cos y$ .