- f(x, y) = x²y³ 20
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
13
Transcribed Image Text: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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