Developmental Mathematics (9th Edition)
9th Edition
ISBN: 9780321997173
Author: Marvin L. Bittinger, Judith A. Beecher
Publisher: PEARSON
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Chapter I, Problem 14ES
To determine
To calculate: The distance between points
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What is the domain and range, thank you !!
Assume a bivariate patch p(u, v) over the unit square [0, 1]² that is given as a tensor product patch where
u-sections (u fixed to some constant û; v varying across [0, 1]) are quadratic polynomials Pu:û(v) = p(û, v)
while v-sections are lines pv:ô (u) = p(u, v). The boundary lines pv:o(u) and pv:1 (u) are specified by their
end points p(0,0) 0.8 and p(1,0) 0.2 as well as p(0, 1) 0.3 and p(1, 1) = 0.8. The boundary
quadratics pu:o(v) and pu:1 (v) interpolate p(0,0.5) = 0.1 and p(1, 0.5) = 0.9 in addition to the above given
four corner-values.
=
=
=
Use Pu:û(v) = (1, v, v² ) Mq (Pu:û(0), Pu:û (0.5), Pu:û(1)) with
Ma
=
1 0 0
-3
4-1
2 4 2
(Pv:ô
as well as pu: (u) = (1, u) M₁ (pv:v (0), P: (1)) with
M₁
=
= (19)
0
to formulate p(u, v) using the "geometric input" G with
G
=
= (P(0,0%)
p(0,0) p(0,0.5) p(0,1)
) = ( 0.39
0.8 0.1 0.3
0.2 0.9 0.8
p(1,0) p(1, 0.5) p(1, 1)
See the figure below for (left) a selection of iso-lines of p(u, v) and (right) a 3D rendering of p(u, v) as a
height surface…
12. Suppose that a, b E R and a < b. Show that the vector space C[a, b] of all continuous complex
valued functions defined on [a, b], with supremum norm
is a Banach space.
Ilflloc:
=
sup f(t),
t€[a,b]
Chapter I Solutions
Developmental Mathematics (9th Edition)
Ch. I - Find the distance between each pair of points....Ch. I - Prob. 2DECh. I - Prob. 3DECh. I - Prob. 4DECh. I - Prob. 1ESCh. I - Prob. 2ESCh. I - Prob. 3ESCh. I - Prob. 4ESCh. I - Prob. 5ESCh. I - Prob. 6ES
Ch. I - Prob. 7ESCh. I - Prob. 8ESCh. I - Prob. 9ESCh. I - Prob. 10ESCh. I - Prob. 11ESCh. I - Prob. 12ESCh. I - Prob. 13ESCh. I - Prob. 14ESCh. I - Prob. 15ESCh. I - Prob. 16ESCh. I - Prob. 17ESCh. I - Prob. 18ESCh. I - Prob. 19ESCh. I - Prob. 20ESCh. I - Prob. 21ESCh. I - Prob. 22ESCh. I - Prob. 23ESCh. I - Prob. 24ESCh. I - Prob. 25ESCh. I - Prob. 26ESCh. I - Prob. 27ESCh. I - Prob. 28ESCh. I - Prob. 29ESCh. I - Prob. 30ESCh. I - Prob. 31ESCh. I - Prob. 32ESCh. I - Prob. 33ESCh. I - Prob. 34ESCh. I - Prob. 35ESCh. I - Prob. 36ESCh. I - Prob. 37ESCh. I - Prob. 38ESCh. I - Prob. 39ESCh. I - Prob. 40ESCh. I - Prob. 41ESCh. I - Prob. 42ESCh. I - Prob. 43ESCh. I - Prob. 44ES
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