2. Consider the curve given by r(0)=2+2 cos 0, 0≤0 ≤2π. (a) Give a rough sketch. (b) Calculate the enclosed area.
2. Consider the curve given by r(0)=2+2 cos 0, 0≤0 ≤2π. (a) Give a rough sketch. (b) Calculate the enclosed area.
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
only question 2 complete please
![1.
(a) Find the equation of the plane PL which contains the three points
A = (1,0,1), B = (-1,2,5), and C= (5,1, -1).
(b) Find the parametric equation of a line L which passes through the origin
and is perpendicular to PL.
2. Consider the curve given by
r(0)=2+2 cos 0, 0≤0 ≤2π.
(a) Give a rough sketch.
(b) Calculate the enclosed area.
3. For the curve
6
= 2 + 6 sin
r(0) =
(a) Find the eccentricity and the directrix.
(b) Describe the curve and provide a sketch.
4. Consider the curve given by
r(t) = (e-t cos(t), e-t sin(t), 1- e-t), t = [0, 2π].
(a) Find the arc length L of this curve.
(b) Find the points (if any) where the curve is parallel to the z-axis?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feac25eb9-213c-4be9-ac5b-c069dffd70f0%2Fd22dea18-e63b-4b6d-819d-12972c809c3a%2Foicwxo2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1.
(a) Find the equation of the plane PL which contains the three points
A = (1,0,1), B = (-1,2,5), and C= (5,1, -1).
(b) Find the parametric equation of a line L which passes through the origin
and is perpendicular to PL.
2. Consider the curve given by
r(0)=2+2 cos 0, 0≤0 ≤2π.
(a) Give a rough sketch.
(b) Calculate the enclosed area.
3. For the curve
6
= 2 + 6 sin
r(0) =
(a) Find the eccentricity and the directrix.
(b) Describe the curve and provide a sketch.
4. Consider the curve given by
r(t) = (e-t cos(t), e-t sin(t), 1- e-t), t = [0, 2π].
(a) Find the arc length L of this curve.
(b) Find the points (if any) where the curve is parallel to the z-axis?
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