Q. 25 In Exercises 21鈥�26, find the d... [FREE SOLUTION]

91影视

Chapter 12: Q. 25 (page 976)

In Exercises 21鈥�26, find the discriminant of the given function.
$f (胃, 蠒) = \cos 胃 \sin 蠒$ .

Short Answer

Expert verified

The answer is $\sin^{2} 蠒 \cos^{2} 胃 - \cos^{2} 蠒 \sin^{2} 胃$ .

Step by step solution

Step 1. Given Information.

The function is $f (胃, 蠒) = \cos 胃 \sin 蠒$ .

Step 2. Explanation.

The discriminant is calculated by formula,

$d e t (H_{f}) = \frac{{鈭�}^{2} f}{鈭� 胃^{2}} 路 \frac{{鈭�}^{2} f}{鈭� 蠒^{2}} - {(\frac{{鈭�}^{2} f}{鈭� 胃鈭� 蠒})}^{2}$ .

Calculate $\frac{鈭� f}{鈭� 胃}$ , $\frac{鈭� f}{鈭� 鈭�}$ , $\frac{{鈭�}^{2} f}{鈭� 胃^{2}}$ , $\frac{{鈭�}^{2} f}{鈭� 蠒^{2}}$ and $\frac{{鈭�}^{2} f}{鈭� 胃鈭� 蠒}$ .

$\frac{鈭� f}{鈭� 胃} = - \sin 胃 \sin 蠒$ , $\frac{{鈭�}^{2} f}{鈭� 胃^{2}} = - \cos 胃 \sin 蠒$ .

localid="1650041459981" $\frac{鈭� f}{鈭� 鈭�} = \cos 蠒 \cos 胃$ , $\frac{{鈭�}^{2} f}{鈭� 蠒^{2}} = - \sin 蠒 \cos 胃$ .

$\frac{{鈭�}^{2} f}{鈭� 胃鈭� 蠒} = - \cos 蠒 \sin 胃$ .

Step 3. Calculation.

Calculate $d e t (H_{f}) = \frac{{鈭�}^{2} f}{鈭� 胃^{2}} 路 \frac{{鈭�}^{2} f}{鈭� 蠒^{2}} - {(\frac{{鈭�}^{2} f}{鈭� 胃鈭� 蠒})}^{2}$ .

role="math" localid="1650042389735" $d e t (H_{f}) = (- \cos 胃 \sin 蠒) (- \sin 蠒 \cos 胃) - {(- \cos 蠒 \sin 胃)}^{2} = \sin^{2} 蠒 \cos^{2} 胃 - \cos^{2} 蠒 \sin^{2} 胃$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

In Exercises 21鈥�26, find the discriminant of the given function.
$f (胃, 蠒) = \cos 胃 \sin 蠒$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Decision Maths

Calculus

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

91影视

In Exercises 21鈥�26, find the discriminant of the given function.f胃,蠒=cos胃sin蠒.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Decision Maths

Calculus

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

In Exercises 21鈥�26, find the discriminant of the given function.
$f (胃, 蠒) = \cos 胃 \sin 蠒$ .