1. 2. If u = x²(x² + y²), find ou/0x, du/dy. If st", find as/at, as/Ou.

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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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Section 1 ,number 1-4 & 3-6
►PROBLEMS, SECTION 1
1.
2.
3.
4.
5.
6.
If u = x²/(x² + y2), find Ju/0x, du/dy.
If st", find əs/at, 08/0u.
If z = ln √u² + v² +w², find əz/au, dz/dv, dz/dw.
For w=a³y³ - 2xy + 6, find a2 w/0x² and 2 w/y² at the points where
Əw/dx = Əw/y = 0.
For w=8a¹ + y - 2xy², find ² w/8² and 0w/y² at the points where
дw/дх= дw/ду = 0.
For u = e cos y,
(a) verify that 0²u/dxdy = ²u/əyəx;
(b) verify that 0²u/0x² +0²u/0y² = 0.
Transcribed Image Text:►PROBLEMS, SECTION 1 1. 2. 3. 4. 5. 6. If u = x²/(x² + y2), find Ju/0x, du/dy. If st", find əs/at, 08/0u. If z = ln √u² + v² +w², find əz/au, dz/dv, dz/dw. For w=a³y³ - 2xy + 6, find a2 w/0x² and 2 w/y² at the points where Əw/dx = Əw/y = 0. For w=8a¹ + y - 2xy², find ² w/8² and 0w/y² at the points where дw/дх= дw/ду = 0. For u = e cos y, (a) verify that 0²u/dxdy = ²u/əyəx; (b) verify that 0²u/0x² +0²u/0y² = 0.
3.
4.
5.
6.
7.
8.
- Lume
If u =
Hint:
Use L'Hôpital's rule to evaluate lim -
1-2 z
= f* sindt, find
Use differentials.
2x-3y du
In u
If
cos sin t
If w=
-
dt, find
ay
If ["e-t
find
=z and u"
dsmu, find
da
da
du
A4
ди ди
Әх' ду da
=y, find
w dw
дх' ду 8x
and
sin t
and at z = π/2, y = π.
du
da
at z = 3, y = 1.
du
dy
dt.
1
a
and
Əy
da
at u = 2, v=0.
Transcribed Image Text:3. 4. 5. 6. 7. 8. - Lume If u = Hint: Use L'Hôpital's rule to evaluate lim - 1-2 z = f* sindt, find Use differentials. 2x-3y du In u If cos sin t If w= - dt, find ay If ["e-t find =z and u" dsmu, find da da du A4 ди ди Әх' ду da =y, find w dw дх' ду 8x and sin t and at z = π/2, y = π. du da at z = 3, y = 1. du dy dt. 1 a and Əy da at u = 2, v=0.
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As per guidelines we are supposed to answer only the first three questions from multipart questions and one from multi-questions.

1)

u = x2(x2+y2)

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