Use a graphing utility to determine the first three points with 020 at which the spiral r = 60 has a horizontal tangent line. Find the first three points with 020 at which the spiral r = 60 has a vertical tangent line. The first point (r,0), with 0≥0, at which the spiral has a horizontal tangent line is (0,0). (Type an ordered pair. Round to one decimal place as needed.) The second point (r,0), with 0≥0, at which the spiral has a horizontal tangent line is.
Use a graphing utility to determine the first three points with 020 at which the spiral r = 60 has a horizontal tangent line. Find the first three points with 020 at which the spiral r = 60 has a vertical tangent line. The first point (r,0), with 0≥0, at which the spiral has a horizontal tangent line is (0,0). (Type an ordered pair. Round to one decimal place as needed.) The second point (r,0), with 0≥0, at which the spiral has a horizontal tangent line is.
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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Question
please find the third point too!

Transcribed Image Text:Use a graphing utility to determine the first three points with 020 at
which the spiral r = 60 has a horizontal tangent line. Find the first
three points with 020 at which the spiral r = 60 has a vertical
tangent line.
The first point (r,0), with 0≥0, at which the spiral has a horizontal
tangent line is (0,0).
(Type an ordered pair. Round to one decimal place as needed.)
The second point (r,0), with 0≥0, at which the spiral has a
horizontal tangent line is.
Expert Solution

Step 1: Equation of tamgent in polar
Let the equation of a curve be
Then the slope of a tangent
For horizontal tangent
and for vertical tangent
Step by step
Solved in 4 steps with 2 images

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