True-False Quiz Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. 5. If f(x, y) → L as (x, y) → (a, b) along every straight line through (a, b), then lim(x, y) → (a, b) ƒ (x, y) = L. f(a, y) – f(a, b) 6. If f.(a, b) and f,(a, b) both exist, then f is differentiable at (a, b). 1. f,(a, b) = lim y – b 2. There exists a function f with continuous second-order partial derivatives such that f:(x, y) = x + y? and f,(x, y) = x – y². 7. If f has a local minimum at (a, b) and ƒ is differentiable at (a, b), then Vf(a, b) = 0. 8. If f is a function, then lim 3. fay = дх ду (x, y2, 5) (x, y) = f(2, 5) 4. Dr.f(x, y, z) = f(x, y, z) 9. If f(x, y) = In y, then Vf(x, y) = 1/y. Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall leaning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 968 CHAPTER 14 PARTIAL DERIVATIVES 10. If (2, 1) is a critical point ofƒ and 11. If f(x, y) = sin x + sin y, then –/2 < Duf(x, y) < /2. far (2, 1) f» (2, 1) < [fy(2, 1)]² 12. If f(x, y) has two local maxima, then f must have a local then f has a saddle point at (2, 1). minimum.
True-False Quiz Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. 5. If f(x, y) → L as (x, y) → (a, b) along every straight line through (a, b), then lim(x, y) → (a, b) ƒ (x, y) = L. f(a, y) – f(a, b) 6. If f.(a, b) and f,(a, b) both exist, then f is differentiable at (a, b). 1. f,(a, b) = lim y – b 2. There exists a function f with continuous second-order partial derivatives such that f:(x, y) = x + y? and f,(x, y) = x – y². 7. If f has a local minimum at (a, b) and ƒ is differentiable at (a, b), then Vf(a, b) = 0. 8. If f is a function, then lim 3. fay = дх ду (x, y2, 5) (x, y) = f(2, 5) 4. Dr.f(x, y, z) = f(x, y, z) 9. If f(x, y) = In y, then Vf(x, y) = 1/y. Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall leaning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 968 CHAPTER 14 PARTIAL DERIVATIVES 10. If (2, 1) is a critical point ofƒ and 11. If f(x, y) = sin x + sin y, then –/2 < Duf(x, y) < /2. far (2, 1) f» (2, 1) < [fy(2, 1)]² 12. If f(x, y) has two local maxima, then f must have a local then f has a saddle point at (2, 1). minimum.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
Related questions
Question
Please Answer
![True-False Quiz
Determine whether the statement is true or false. If it is true, explain why.
If it is false, explain why or give an example that disproves the statement.
5. If f(x, y) → L as (x, y) → (a, b) along every straight line
through (a, b), then lim(x, y)>(a, b) f(x, y) = L.
f(a, y) – f(a, b)
6. If f.(a, b) and f,(a, b) both exist, then f is differentiable
at (a, b).
1. f,(a, b)
= lim
y – b
2. There exists a function f with continuous second-order
partial derivatives such that f.(x, y) = x + y² and
f,(x, y) = x – y².
7. If f has a local minimum at (a, b) and f is differentiable at
(a, b), then Vf(a, b) = 0.
8. If f is a function, then
3. fry
lim f(x, y) = f(2, 5)
дх ду
(х, у) — (2, 5)*
4. Dk f(x, y, z) = f:(x, y, z)
9. If f(x, y) = In y, then Vf(x, y) = 1/y.
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does:
materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
968
CHAPTER 14 PARTIAL DERIVATIVES
10. If (2, 1) is a critical point of f and
11. If f(x, y) = sin x + sin y, then –/2 < Duƒ(x, y) < /2.
fa:(2, 1) fyy(2, 1) < [fxy(2, 1)]²
12. If f(x, y) has two local maxima, then f must have a local
then f has a saddle point at (2, 1).
minimum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2452a393-14a3-4447-acfc-84002daf23c9%2F511656fc-bd3a-4dbc-8631-1ba802d50f09%2F1boa9p5_processed.png&w=3840&q=75)
Transcribed Image Text:True-False Quiz
Determine whether the statement is true or false. If it is true, explain why.
If it is false, explain why or give an example that disproves the statement.
5. If f(x, y) → L as (x, y) → (a, b) along every straight line
through (a, b), then lim(x, y)>(a, b) f(x, y) = L.
f(a, y) – f(a, b)
6. If f.(a, b) and f,(a, b) both exist, then f is differentiable
at (a, b).
1. f,(a, b)
= lim
y – b
2. There exists a function f with continuous second-order
partial derivatives such that f.(x, y) = x + y² and
f,(x, y) = x – y².
7. If f has a local minimum at (a, b) and f is differentiable at
(a, b), then Vf(a, b) = 0.
8. If f is a function, then
3. fry
lim f(x, y) = f(2, 5)
дх ду
(х, у) — (2, 5)*
4. Dk f(x, y, z) = f:(x, y, z)
9. If f(x, y) = In y, then Vf(x, y) = 1/y.
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does:
materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
968
CHAPTER 14 PARTIAL DERIVATIVES
10. If (2, 1) is a critical point of f and
11. If f(x, y) = sin x + sin y, then –/2 < Duƒ(x, y) < /2.
fa:(2, 1) fyy(2, 1) < [fxy(2, 1)]²
12. If f(x, y) has two local maxima, then f must have a local
then f has a saddle point at (2, 1).
minimum.
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