Consider the function f and region E. 1 , E = {(x, y, z) | 0 ≤ x² + y² ≤ 9, x ≥ 0, y ≥ 0,0 ≤ z ≤ x + 3} x + 3 f(x, y, z) (a) Express the region E in cylindrical coordinates. O E = {(r, 0, z) |0 ≤ r ≤ 9,0 ≤ 0 ≤ 1,0 ≤ z ≤ sin(0) + +3} 2 O E = {(r, 0, z) | 0 ≤ r ≤ 3,0 ≤ 0 ≤ π, 0 ≤ z ≤ sin(0) + 3} E = {(r, 0, z) |0 ≤ r ≤ 3,0 ≤ 0 ≤ TI 511,0525 (b) Convert the integral 0 ≤z ≤r cos(0) + 3 ΟΕ E = {(r, 0, z) |0 ≤ r ≤ 3,0 ≤ e s. ≤ 0 ≤ 1,0 ≤ z ≤ cos(0) + 3} O E = {(r, 0, z) |0 ≤ r ≤ 9,0 ≤ 0 ≤ π, 0 ≤ z ≤ cos(0) + 3} Express the function f in cylindrical coordinates. f(r, 0, z) = III. f(x, y, z) dV into cylindrical coordinates and evaluate it.
Consider the function f and region E. 1 , E = {(x, y, z) | 0 ≤ x² + y² ≤ 9, x ≥ 0, y ≥ 0,0 ≤ z ≤ x + 3} x + 3 f(x, y, z) (a) Express the region E in cylindrical coordinates. O E = {(r, 0, z) |0 ≤ r ≤ 9,0 ≤ 0 ≤ 1,0 ≤ z ≤ sin(0) + +3} 2 O E = {(r, 0, z) | 0 ≤ r ≤ 3,0 ≤ 0 ≤ π, 0 ≤ z ≤ sin(0) + 3} E = {(r, 0, z) |0 ≤ r ≤ 3,0 ≤ 0 ≤ TI 511,0525 (b) Convert the integral 0 ≤z ≤r cos(0) + 3 ΟΕ E = {(r, 0, z) |0 ≤ r ≤ 3,0 ≤ e s. ≤ 0 ≤ 1,0 ≤ z ≤ cos(0) + 3} O E = {(r, 0, z) |0 ≤ r ≤ 9,0 ≤ 0 ≤ π, 0 ≤ z ≤ cos(0) + 3} Express the function f in cylindrical coordinates. f(r, 0, z) = III. f(x, y, z) dV into cylindrical coordinates and evaluate it.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the function f and region E.
1
x + 3
f(x, y, z):
=
(a) Express the region E in cylindrical coordinates.
O E=(r, 0, z) 0 ≤ r ≤ 9,0
= {(r₁ , 2) |0 ≤r
ΟΕ
=
‚ E = {(x, y, z) | 0 ≤ x² + y² ≤ 9, x ≥ 0, y ≥ 0, 0 ≤ z ≤ x + 3}
T
OE=
π
osas = 21
≤0 ≤.
{(r, 0, z) |0 ≤ r ≤ 3,0 ≤ 0 ≤ π, 0 ≤ z ≤ sin(0) + 3}
E = {(r, 0, 2) |0 ≤ r
(b) Convert the integral
-3}
0 ≤ z ≤ sin(0) +
=
= {(r, 0, z) |0 ≤ r ≤ 3,0 ≤ 0 ≤t 0 ≤Z< cos(8) + 3
3}
T
2
O E = {(r, 0, z) | 0 ≤ r ≤ 9,0 ≤ 0 ≤ π,0 ≤ z ≤cos(0) + 3}
Express the function f in cylindrical coordinates.
f(r, 0, z) =
≤ r ≤ 3,0 ≤ 0 < 7,0 ≤ z ≤r cos(0) + 3
JIJE f(x, y, z) dV into cylindrical coordinates and evaluate it.
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