Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 10, Problem 4SP
To determine
To find: the
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Problem 2. Now consider the relation D' on the domain Z+ where xD'y if and only if æ|y. Use the
properties of functions and the relation between them to answer the following questions and to reach a
conclusion about (Z+, D').
2(a) Prove that D' is reflexive.
2(b) Prove that D' is anti-symmetric.
2(c) Prove that D' is transitive.
4. b)
7. In this problem, we prove that a straight line is the shortest curve between two points in
R. Let p, q E Rª and let r be a curve such that r(to) = p and r(t1) = q, where to < t1.
(a) Show that, if u is any unit vector in Rd, the r'(t) · u < ||r'(t)|| for all t.
• u
(b) Show that
(q – p) · u < / ||r (t)||dt.
to
1
(c) Show that the arc length of r from r(to) to r(t1) is at least ||q- p||. Hint: Consider
a well-chosen unit vector u.
Chapter 10 Solutions
Calculus
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