Use the Wallis sine and cosine formulas: ∫ 0 π / 2 sin n x d x = π 2 ⋅ 1 ⋅ 3 ⋅ 5 ⋅ ⋅ ⋅ n − 1 2 ⋅ 4 ⋅ 6 ⋅ ⋅ ⋅ n n even and ≥ 2 ∫ 0 π / 2 sin n x d x = 2 ⋅ 4 ⋅ 6 ⋅ ⋅ ⋅ n − 1 3 ⋅ 5 ⋅ 7 ⋅ ⋅ ⋅ n n odd and ≥ 3 ∫ 0 π / 2 cos n x d x = π 2 ⋅ 1 ⋅ 3 ⋅ 5 ⋅ ⋅ ⋅ n − 1 2 ⋅ 4 ⋅ 6 ⋅ ⋅ ⋅ n n even and ≥ 2 ∫ 0 π / 2 cos n x d x = 2 ⋅ 4 ⋅ 6 ⋅ ⋅ ⋅ n − 1 3 ⋅ 5 ⋅ 7 ⋅ ⋅ ⋅ n n odd and ≥ 3 Find the mass of the solid in the first octant bounded above by the paraboloid z = 4 − x 2 − y 2 , below by the plane z = 0 , and laterally by the cylinder x 2 + y 2 = 2 x and the plane y = 0 assuming the density to be δ x , y , z = z .
Use the Wallis sine and cosine formulas: ∫ 0 π / 2 sin n x d x = π 2 ⋅ 1 ⋅ 3 ⋅ 5 ⋅ ⋅ ⋅ n − 1 2 ⋅ 4 ⋅ 6 ⋅ ⋅ ⋅ n n even and ≥ 2 ∫ 0 π / 2 sin n x d x = 2 ⋅ 4 ⋅ 6 ⋅ ⋅ ⋅ n − 1 3 ⋅ 5 ⋅ 7 ⋅ ⋅ ⋅ n n odd and ≥ 3 ∫ 0 π / 2 cos n x d x = π 2 ⋅ 1 ⋅ 3 ⋅ 5 ⋅ ⋅ ⋅ n − 1 2 ⋅ 4 ⋅ 6 ⋅ ⋅ ⋅ n n even and ≥ 2 ∫ 0 π / 2 cos n x d x = 2 ⋅ 4 ⋅ 6 ⋅ ⋅ ⋅ n − 1 3 ⋅ 5 ⋅ 7 ⋅ ⋅ ⋅ n n odd and ≥ 3 Find the mass of the solid in the first octant bounded above by the paraboloid z = 4 − x 2 − y 2 , below by the plane z = 0 , and laterally by the cylinder x 2 + y 2 = 2 x and the plane y = 0 assuming the density to be δ x , y , z = z .
∫
0
π
/
2
sin
n
x
d
x
=
π
2
⋅
1
⋅
3
⋅
5
⋅
⋅
⋅
n
−
1
2
⋅
4
⋅
6
⋅
⋅
⋅
n
n
even
and
≥
2
∫
0
π
/
2
sin
n
x
d
x
=
2
⋅
4
⋅
6
⋅
⋅
⋅
n
−
1
3
⋅
5
⋅
7
⋅
⋅
⋅
n
n
odd
and
≥
3
∫
0
π
/
2
cos
n
x
d
x
=
π
2
⋅
1
⋅
3
⋅
5
⋅
⋅
⋅
n
−
1
2
⋅
4
⋅
6
⋅
⋅
⋅
n
n
even
and
≥
2
∫
0
π
/
2
cos
n
x
d
x
=
2
⋅
4
⋅
6
⋅
⋅
⋅
n
−
1
3
⋅
5
⋅
7
⋅
⋅
⋅
n
n
odd
and
≥
3
Find the mass of the solid in the first octant bounded above by the paraboloid
z
=
4
−
x
2
−
y
2
,
below by the plane
z
=
0
,
and laterally by the cylinder
x
2
+
y
2
=
2
x
and the plane
y
=
0
assuming the density to be
δ
x
,
y
,
z
=
z
.
Decide whether each limit exists. If a limit exists, estimate its
value.
11. (a) lim f(x)
x-3
f(x) ↑
4
3-
2+
(b) lim f(x)
x―0
-2
0
X
1234
Determine whether the lines
L₁ (t) = (-2,3, −1)t + (0,2,-3) and
L2 p(s) = (2, −3, 1)s + (-10, 17, -8)
intersect. If they do, find the point of intersection.
Convert the line given by the parametric equations y(t)
Enter the symmetric equations in alphabetic order.
(x(t)
= -4+6t
= 3-t
(z(t)
=
5-7t
to symmetric equations.
Chapter 14 Solutions
Calculus Early Transcendentals, Binder Ready Version
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Trigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,