4. Find a parametric form of the curve given by 2r + 3y? - 6r + 6y + = 0 in the ry-plane with a counterclockwise orientation. 5. Parametrize the following hyperbolae: (a) 2r – 4y? = 8 (b) y? - r2 = 1
4. Find a parametric form of the curve given by 2r + 3y? - 6r + 6y + = 0 in the ry-plane with a counterclockwise orientation. 5. Parametrize the following hyperbolae: (a) 2r – 4y? = 8 (b) y? - r2 = 1
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![1. (Equality in Cauch Cchwarz,
have equality in the Cauchy-Schwarz inequality
Let x, y € R" be non-zero vectors. Show that we
x y = |x||y|
if and only if there exists c eR such that x = cy. (Hint: for the direction, consider the
norm difference |x - cy/?).
2. (Reverse triangle inequality,
Prove that ||x| – ly|| < |x - y| for every x.y € R".
3. Let x € R".
Prove that |xmax < |x| < Vīx|max
Show that |x| < x|ı < Vn|x, where |x]1 = E ri|.
(a) (VIP,
(Ь)
%3D
1
4.
Find a parametric form of the curve given by 2r + 3y? – 6x + 6y + = 0 in the
4
ry-plane with a counterclockwise orientation.
5. Parametrize the following hyperbolae:
(a)
2.r – 4y? = 8
(b)
y? - r2 = 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbfdf6ea7-0ba1-4433-aba1-e1b8f996d129%2F2b34caae-8b17-4e3b-8ece-e0cfb63f354e%2Fifkusnq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. (Equality in Cauch Cchwarz,
have equality in the Cauchy-Schwarz inequality
Let x, y € R" be non-zero vectors. Show that we
x y = |x||y|
if and only if there exists c eR such that x = cy. (Hint: for the direction, consider the
norm difference |x - cy/?).
2. (Reverse triangle inequality,
Prove that ||x| – ly|| < |x - y| for every x.y € R".
3. Let x € R".
Prove that |xmax < |x| < Vīx|max
Show that |x| < x|ı < Vn|x, where |x]1 = E ri|.
(a) (VIP,
(Ь)
%3D
1
4.
Find a parametric form of the curve given by 2r + 3y? – 6x + 6y + = 0 in the
4
ry-plane with a counterclockwise orientation.
5. Parametrize the following hyperbolae:
(a)
2.r – 4y? = 8
(b)
y? - r2 = 1
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