7 S9245-8 Determine the signs of the partial derivatives for thefunction f whose graph is shown.nom mofed boekemoni ridZAcels ai noilbolbus 18 x5. (a) f(1, 2)6. (a) f(-1,2)7. (a) f(-1,2)8. (a) fry (1, 2)2CHAPTER 14 Partial DerivativesZO(3.149. The following surfaces, labeled a, b, and c, are graphs of afunction f and its partial derivatives fr and fy. Identify eachsurface and give reasons for your choices.z 0+-48-4-0 base-4--8--3 -2 -1 0 1 2y$2 ni boreuosib ow ind8-9041sida atwo-3 -2 -1 0yCI1b2(b) f,(1, 2)(b) f(-1,2)ZO-4-8-3 -2 -1 0 1 2y 10(b) fyy(-1,2)(b) fxy(-1,2)3DEto put odi seC3323rgia avs220s oniw sdt toni ti babroo-2X-20X202(etonut) booqe baiy6 bocmila (d)fr(2, 1) and f,(2, 1).10. A contour map is given for a function f. Use it to estimateYA-223bril mont(2,3mmens13. f(x, y) = x²y³dal21. f(x, y) =0msw 21 tuos15. f(x, y) = x² + 5xy³muoe ban 12517. f(x, t) = t²e-X19. z = ln(x + t²)XTo willon11. If f(x, y) = 16 - 4x² - y², find fr(1, 2) and fy(1, 2) andinterpret these numbers as slopes. Illustrate with either hand-drawn sketches or computer plots.12. If f(x, y) = √√4x² - 4y², find fx(1, 0) and f,(1, 0) andinterpret these numbers as slopes. Illustrate with either hand-drawn sketches or computer plots.X ENTbasation by thebecauszib sw13-14 Find fx and fy and graph f, fx, and fy with domains andviewpoints that enable you to see the relationships between them.yHi ai Txabaiax + by T SUs6 823. f(x, y) =anolla taquica iscx + dy25. g(u, v) = (u²v – v³)527. R(p, q) = tan¯¹(pq²)316 bas15-40 Find the first partial derivatives of the function. H (d)qe bat29. F(x, y) = f* cos(e¹) dt1031. f(x, y, z) = x³yz² + 2yz(g) be=In(x + 2y + 3z)33. w35. p = √t + u² cos v37. h(x, y, z, t) = x²y cos(z/t)39. u = √√x² + x² + ... +40. u = sin(x₁ + 2x₂ +24612161822. f(x, y) = -medodrxabai med odreisdw (1)x)²14. f(x, y)+ x ²2/…+nx)=16. f(x, y) = x²y - 3y4odhon18. f(x, t) = √3x + 4t20. z = x sin(xy)1sdW000) u +34. w=y1 + x²y²JpdW41-44 Find the indicated partial derivative.eº24. wei A bmv²u + v² sein26. u(r,0) = sin(r cos 0)f(x, y) = x³Tasuwith(x + y)²28.8. Jsquat lacosavijXB30. F(a, B) = √√√₁³ + 1 dt1.Al moitoo2 da I sidst32. f(x, y, z) = xy²e-x²36. u = xy/z38. (x, y, z, t)AMF= y tan(x + 2z)41. R(s, t) = test; R,(0, 1) lasing n179ax + By²yz +81²amat LESA-lo asulay sdi stemitz (0)

SOLUTION - 5-8 Given level curve,

Answered: 1.1 nouss2 ni boze 5. (a) f(1, 2) 6.…

1.1 nouss2 ni boze 5. (a) f(1, 2) 6. (a) f(-1, 2) 7. (a) f(-1,2) 8. (a) fry (1, 2) (b) f(1, 2) (b) f(-1,2) (b) fyy(-1,2) (b) f(-1,2)

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Operations

In mathematics and computer science, an operation is an event that is carried out to satisfy a given task. Basic operations of a computer system are input, processing, output, storage, and control.

Basic Operators

An operator is a symbol that indicates an operation to be performed. We are familiar with operators in mathematics; operators used in computer programming are—in many ways—similar to mathematical operators.

Division Operator

We all learnt about division—and the division operator—in school. You probably know of both these symbols as representing division:

Modulus Operator

Modulus can be represented either as (mod or modulo) in computing operation. Modulus comes under arithmetic operations. Any number or variable which produces absolute value is modulus functionality. Magnitude of any function is totally changed by modulo operator as it changes even negative value to positive.

Operators

In the realm of programming, operators refer to the symbols that perform some function. They are tasked with instructing the compiler on the type of action that needs to be performed on the values passed as operands. Operators can be used in mathematical formulas and equations. In programming languages like Python, C, and Java, a variety of operators are defined.

Question

S
924
5-8 Determine the signs of the partial derivatives for the
function f whose graph is shown.
nom mof
ed boekemoni rid
ZA
cels ai noilbol
bus 18 x
5. (a) f(1, 2)
6. (a) f(-1,2)
7. (a) f(-1,2)
8. (a) fry (1, 2)
2
CHAPTER 14 Partial Derivatives
ZO
(3.1
4
9. The following surfaces, labeled a, b, and c, are graphs of a
function f and its partial derivatives fr and fy. Identify each
surface and give reasons for your choices.
z 0+
-4
8-
4-0 base
-4-
-8-
-3 -2 -1 0 1 2
y
$2 ni boreuosib ow ind
8-90
41
sida atwo
-3 -2 -1 0
y
CI
1
b
2
(b) f,(1, 2)
(b) f(-1,2)
ZO
-4
-8
-3 -2 -1 0 1 2
y 10
(b) fyy(-1,2)
(b) fxy(-1,2)
3
DE
to put odi se
C
3
3
23rgia avs
2
20
s oniw sdt to
ni ti babroo
-2
X
-2
0
X
202
(etonut) booqe baiy
6 boc
mila (d)
fr(2, 1) and f,(2, 1).
10. A contour map is given for a function f. Use it to estimate
YA
-2
2
3
bril mont
(2,3mmens
13. f(x, y) = x²y³
dal
21. f(x, y) =
0
msw 21 tuos
15. f(x, y) = x² + 5xy³
muoe ban 125
17. f(x, t) = t²e
-X
19. z = ln(x + t²)
X
To will
on
11. If f(x, y) = 16 - 4x² - y², find fr(1, 2) and fy(1, 2) and
interpret these numbers as slopes. Illustrate with either hand-
drawn sketches or computer plots.
12. If f(x, y) = √√4x² - 4y², find fx(1, 0) and f,(1, 0) and
interpret these numbers as slopes. Illustrate with either hand-
drawn sketches or computer plots.X ENT
bas
ation by the
becauszib sw
13-14 Find fx and fy and graph f, fx, and fy with domains and
viewpoints that enable you to see the relationships between them.
y
H
i ai Txabai
ax + by T SU
s
6 8
23. f(x, y) =
anolla taquica iscx + dy
25. g(u, v) = (u²v – v³)5
27. R(p, q) = tan¯¹(pq²)
3
16 bas
15-40 Find the first partial derivatives of the function. H (d)
qe bat
29. F(x, y) = f* cos(e¹) dt
10
31. f(x, y, z) = x³yz² + 2yz
(g) be
=
In(x + 2y + 3z)
33. w
35. p = √t + u² cos v
37. h(x, y, z, t) = x²y cos(z/t)
39. u = √√x² + x² + ... +
40. u = sin(x₁ + 2x₂ +
246
12
16
18
22. f(x, y) = -
med
odr
xabai med odreisdw (1)
x)²
14. f(x, y)
+ x ²2/
…+nx)
=
16. f(x, y) = x²y - 3y4
odhon
18. f(x, t) = √3x + 4t
20. z = x sin(xy)
1sdW000) u +
34. w=
y
1 + x²y²
JpdW
41-44 Find the indicated partial derivative.
eº
24. wei A bm
v²
u + v² sein
26. u(r,0) = sin(r cos 0)
f(x, y) = x³
Tasu
with
(x + y)²
28.
8. Jsquat lacos
avij
X
B
30. F(a, B) = √√√₁³ + 1 dt
1.Al moitoo2 da I sidst
32. f(x, y, z) = xy²e-x²
36. u = xy/z
38. (x, y, z, t)
AMF
= y tan(x + 2z)
41. R(s, t) = test; R,(0, 1) lasing n
179
ax + By²
yz +81²
amat LESA
-lo asulay sdi stemitz (0)

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