Find the arc length of the spiral as 0 varies from 0 = – ∞ to 0 = 0. Are you ready for this?! You're about to find the length of an arc that starts from a radius of 1 and spirals infinitely many times into the origin. %3D
Find the arc length of the spiral as 0 varies from 0 = – ∞ to 0 = 0. Are you ready for this?! You're about to find the length of an arc that starts from a radius of 1 and spirals infinitely many times into the origin. %3D
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
![Consider the curve r = e
°.
Note that as 0 approaches – ∞, the radius: e° approaches 0.
This means as 0 rotates clockwise, the radius shrinks ever smaller, and the spiral winds infinitely tighter,
infinitely many times about the origin.
It doesn't look like it though, unless you zoom in. Try zooming in to the origin here:
Logarithmic Spiral Zoom
1
+
Click the << at the top of
this menu to get this out
of the way.
-2
2
= e0
r =
1-
-100 <0< 0
3
-1
1.
2.
-1-
-2
-3
powered by
desmos
Find the arc length of the spiral as 0 varies from 0 = - ∞ to 0 = 0.
Are you ready for this?! You're about to find the length of an arc that starts from a radius of 1 and spirals
infinitely many times into the origin.
s =
Evaluate by hand and give exact answer: no decimals.
of
II](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8118b3cc-2b06-46e5-9a0e-5c7e6db971ab%2F4276367e-b37d-4e9d-938e-3bc67445619d%2Ffz1f51k_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the curve r = e
°.
Note that as 0 approaches – ∞, the radius: e° approaches 0.
This means as 0 rotates clockwise, the radius shrinks ever smaller, and the spiral winds infinitely tighter,
infinitely many times about the origin.
It doesn't look like it though, unless you zoom in. Try zooming in to the origin here:
Logarithmic Spiral Zoom
1
+
Click the << at the top of
this menu to get this out
of the way.
-2
2
= e0
r =
1-
-100 <0< 0
3
-1
1.
2.
-1-
-2
-3
powered by
desmos
Find the arc length of the spiral as 0 varies from 0 = - ∞ to 0 = 0.
Are you ready for this?! You're about to find the length of an arc that starts from a radius of 1 and spirals
infinitely many times into the origin.
s =
Evaluate by hand and give exact answer: no decimals.
of
II
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