a) The parameterization of the curve on the surface of the sphere with 0 (t) of the spherical radius R is given by the angles & = (t) and 0 = coordinate system, when t = [a, b]. Prove that an expression can be obtained for the arc length of the curve ·b [{"* |r′(1)\ dt = f*°* √\x²′(1)² + y'′(1)² + z'(t)}² dt = R 2 √ (1)² + sin² (1) · 0¹ (1) ² dt. b) According to the latest research by a docent on duty at the equator, the equator has bulged due to thermal expansion due to climate change Calculate its approximate length in case R = 1. ㅠ +0,1 cos(10t), 0=t, 0≤ t ≤ 2π. 2
a) The parameterization of the curve on the surface of the sphere with 0 (t) of the spherical radius R is given by the angles & = (t) and 0 = coordinate system, when t = [a, b]. Prove that an expression can be obtained for the arc length of the curve ·b [{"* |r′(1)\ dt = f*°* √\x²′(1)² + y'′(1)² + z'(t)}² dt = R 2 √ (1)² + sin² (1) · 0¹ (1) ² dt. b) According to the latest research by a docent on duty at the equator, the equator has bulged due to thermal expansion due to climate change Calculate its approximate length in case R = 1. ㅠ +0,1 cos(10t), 0=t, 0≤ t ≤ 2π. 2
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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![a) The parameterization
of the curve on the surface of the sphere with
e(t) of the spherical
radius R is given by the angles = (t) and
coordinate system, when t € [a, b]. Prove that an expression can be
obtained for the arc length of the curve
·b
[ * \r\(1)\ dt = [°® √√x (1)² + v′(0)² + 2¹(0)³² di
=
a
=
=
R
√√√(t)² + sin² (t) · 0¹ (t)² dt.
b) According to the latest research by a docent on duty at the equator,
the equator has bulged due to thermal expansion due to climate change
Calculate its approximate length in case R = 1.
+0,1 cos(10t), 0 = t, 0 ≤ t ≤ 2π.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4908425-6b77-4ea0-88fa-d88faee532f6%2F68e7c10a-c8d6-44c9-bc54-6f7da7b1381f%2F9hrik93_processed.png&w=3840&q=75)
Transcribed Image Text:a) The parameterization
of the curve on the surface of the sphere with
e(t) of the spherical
radius R is given by the angles = (t) and
coordinate system, when t € [a, b]. Prove that an expression can be
obtained for the arc length of the curve
·b
[ * \r\(1)\ dt = [°® √√x (1)² + v′(0)² + 2¹(0)³² di
=
a
=
=
R
√√√(t)² + sin² (t) · 0¹ (t)² dt.
b) According to the latest research by a docent on duty at the equator,
the equator has bulged due to thermal expansion due to climate change
Calculate its approximate length in case R = 1.
+0,1 cos(10t), 0 = t, 0 ≤ t ≤ 2π.
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