APPLIED CALCULUS (WILEY PLUS)
6th Edition
ISBN: 9781119399322
Author: Hughes-Hallett
Publisher: WILEY
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Chapter 9.1, Problem 9P
To determine
To find:
Adifferential equationforamount of alcohol,
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3.
Consider the sequences of functions f₁: [-π, π] → R,
sin(n²x)
An(2)
n
f pointwise as
(i) Find a function ƒ : [-T,π] → R such that fn
n∞. Further, show that fn →f uniformly on [-π,π] as n → ∞.
[20 Marks]
(ii) Does the sequence of derivatives f(x) has a pointwise limit on [-7, 7]?
Justify your answer.
[10 Marks]
1. (i) Give the definition of a metric on a set X.
[5 Marks]
(ii) Let X = {a, b, c} and let a function d : XxX → [0, ∞) be defined
as d(a, a) = d(b,b) = d(c, c) 0, d(a, c) = d(c, a) 1, d(a, b) = d(b, a) = 4,
d(b, c) = d(c,b) = 2. Decide whether d is a metric on X. Justify your answer.
=
(iii) Consider a metric space (R, d.), where
=
[10 Marks]
0
if x = y,
d* (x, y)
5
if xy.
In the metric space (R, d*), describe:
(a) open ball B2(0) of radius 2 centred at 0;
(b) closed ball B5(0) of radius 5 centred at 0;
(c) sphere S10 (0) of radius 10 centred at 0.
[5 Marks]
[5 Marks]
[5 Marks]
(c) sphere S10 (0) of radius 10 centred at 0.
[5 Marks]
2. Let C([a, b]) be the metric space of continuous functions on the interval
[a, b] with the metric
doo (f,g)
=
max f(x)g(x)|.
xЄ[a,b]
= 1x. Find:
Let f(x) = 1 - x² and g(x):
(i) do(f, g) in C'([0, 1]);
(ii) do(f,g) in C([−1, 1]).
[20 Marks]
[20 Marks]
Chapter 9 Solutions
APPLIED CALCULUS (WILEY PLUS)
Ch. 9.1 - Prob. 1PCh. 9.1 - Prob. 2PCh. 9.1 - Prob. 3PCh. 9.1 - Prob. 4PCh. 9.1 - Prob. 5PCh. 9.1 - Prob. 6PCh. 9.1 - Prob. 7PCh. 9.1 - Prob. 8PCh. 9.1 - Prob. 9PCh. 9.1 - Prob. 10P
Ch. 9.1 - Prob. 11PCh. 9.1 - Prob. 12PCh. 9.1 - Prob. 13PCh. 9.1 - Prob. 14PCh. 9.1 - Prob. 15PCh. 9.1 - Prob. 16PCh. 9.2 - Prob. 1PCh. 9.2 - Prob. 2PCh. 9.2 - Prob. 3PCh. 9.2 - Prob. 4PCh. 9.2 - Prob. 5PCh. 9.2 - Prob. 6PCh. 9.2 - Prob. 7PCh. 9.2 - Prob. 8PCh. 9.2 - Prob. 9PCh. 9.2 - Prob. 10PCh. 9.2 - Prob. 11PCh. 9.2 - Prob. 12PCh. 9.2 - Prob. 13PCh. 9.2 - Prob. 14PCh. 9.2 - Prob. 15PCh. 9.2 - Prob. 16PCh. 9.2 - Prob. 17PCh. 9.2 - Prob. 18PCh. 9.2 - Prob. 19PCh. 9.2 - Prob. 20PCh. 9.2 - Prob. 21PCh. 9.2 - Prob. 22PCh. 9.3 - Prob. 1PCh. 9.3 - Prob. 2PCh. 9.3 - Prob. 3PCh. 9.3 - Prob. 4PCh. 9.3 - Prob. 5PCh. 9.3 - Prob. 6PCh. 9.3 - Prob. 7PCh. 9.3 - Prob. 8PCh. 9.3 - Prob. 9PCh. 9.3 - Prob. 10PCh. 9.3 - Prob. 11PCh. 9.3 - Prob. 12PCh. 9.3 - Prob. 13PCh. 9.3 - Prob. 14PCh. 9.3 - Prob. 15PCh. 9.3 - Prob. 16PCh. 9.3 - Prob. 17PCh. 9.4 - Prob. 1PCh. 9.4 - Prob. 2PCh. 9.4 - Prob. 3PCh. 9.4 - Prob. 4PCh. 9.4 - Prob. 5PCh. 9.4 - Prob. 6PCh. 9.4 - Prob. 7PCh. 9.4 - Prob. 8PCh. 9.4 - Prob. 9PCh. 9.4 - Prob. 10PCh. 9.4 - Prob. 11PCh. 9.4 - Prob. 12PCh. 9.4 - Prob. 13PCh. 9.4 - Prob. 14PCh. 9.4 - Prob. 15PCh. 9.4 - Prob. 16PCh. 9.4 - Prob. 17PCh. 9.5 - Prob. 1PCh. 9.5 - Prob. 2PCh. 9.5 - Prob. 3PCh. 9.5 - Prob. 4PCh. 9.5 - Prob. 5PCh. 9.5 - Prob. 6PCh. 9.5 - Prob. 7PCh. 9.5 - Prob. 8PCh. 9.5 - Prob. 9PCh. 9.5 - Prob. 10PCh. 9.5 - Prob. 11PCh. 9.5 - Prob. 12PCh. 9.5 - Prob. 13PCh. 9.5 - Prob. 14PCh. 9.5 - Prob. 15PCh. 9.5 - Prob. 16PCh. 9.5 - Prob. 17PCh. 9.5 - Prob. 18PCh. 9.5 - Prob. 19PCh. 9.5 - Prob. 20PCh. 9.5 - Prob. 21PCh. 9.5 - Prob. 22PCh. 9.5 - Prob. 23PCh. 9.5 - Prob. 24PCh. 9.5 - Prob. 25PCh. 9.6 - Prob. 1PCh. 9.6 - Prob. 2PCh. 9.6 - Prob. 3PCh. 9.6 - Prob. 4PCh. 9.6 - Prob. 5PCh. 9.6 - Prob. 6PCh. 9.6 - Prob. 7PCh. 9.6 - Prob. 8PCh. 9.6 - Prob. 9PCh. 9.6 - Prob. 10PCh. 9.6 - Prob. 11PCh. 9.6 - Prob. 12PCh. 9.6 - Prob. 13PCh. 9.6 - Prob. 14PCh. 9.6 - Prob. 15PCh. 9.6 - Prob. 16PCh. 9.6 - Prob. 17PCh. 9.6 - Prob. 18PCh. 9.6 - Prob. 19PCh. 9.6 - Prob. 20PCh. 9.6 - Prob. 21PCh. 9.6 - Prob. 22PCh. 9.6 - Prob. 23PCh. 9.6 - Prob. 24PCh. 9.6 - Prob. 25PCh. 9.6 - Prob. 26PCh. 9.7 - Prob. 1PCh. 9.7 - Prob. 2PCh. 9.7 - Prob. 3PCh. 9.7 - Prob. 4PCh. 9.7 - Prob. 5PCh. 9.7 - Prob. 6PCh. 9.7 - Prob. 7PCh. 9.7 - Prob. 8PCh. 9.7 - Prob. 9PCh. 9.7 - Prob. 10PCh. 9.7 - Prob. 11PCh. 9.7 - Prob. 12PCh. 9 - Prob. 1SYUCh. 9 - Prob. 2SYUCh. 9 - Prob. 3SYUCh. 9 - Prob. 4SYUCh. 9 - Prob. 5SYUCh. 9 - Prob. 6SYUCh. 9 - Prob. 7SYUCh. 9 - Prob. 8SYUCh. 9 - Prob. 9SYUCh. 9 - Prob. 10SYUCh. 9 - Prob. 11SYUCh. 9 - Prob. 12SYUCh. 9 - Prob. 13SYUCh. 9 - Prob. 14SYUCh. 9 - Prob. 15SYUCh. 9 - Prob. 16SYUCh. 9 - Prob. 17SYUCh. 9 - Prob. 18SYUCh. 9 - Prob. 19SYUCh. 9 - Prob. 20SYUCh. 9 - Prob. 21SYUCh. 9 - Prob. 22SYUCh. 9 - Prob. 23SYUCh. 9 - Prob. 24SYUCh. 9 - Prob. 25SYUCh. 9 - Prob. 26SYUCh. 9 - Prob. 27SYUCh. 9 - Prob. 28SYUCh. 9 - Prob. 29SYUCh. 9 - Prob. 30SYUCh. 9 - Prob. 31SYUCh. 9 - Prob. 32SYUCh. 9 - Prob. 33SYUCh. 9 - Prob. 34SYUCh. 9 - Prob. 35SYUCh. 9 - Prob. 36SYUCh. 9 - Prob. 37SYUCh. 9 - Prob. 38SYUCh. 9 - Prob. 39SYUCh. 9 - Prob. 40SYUCh. 9 - Prob. 41SYUCh. 9 - Prob. 42SYUCh. 9 - Prob. 43SYUCh. 9 - Prob. 44SYUCh. 9 - Prob. 45SYUCh. 9 - Prob. 46SYUCh. 9 - Prob. 47SYUCh. 9 - Prob. 48SYUCh. 9 - Prob. 49SYUCh. 9 - Prob. 50SYUCh. 9 - Prob. 51SYUCh. 9 - Prob. 52SYUCh. 9 - Prob. 53SYUCh. 9 - Prob. 54SYUCh. 9 - Prob. 55SYUCh. 9 - Prob. 56SYUCh. 9 - Prob. 57SYUCh. 9 - Prob. 58SYUCh. 9 - Prob. 59SYUCh. 9 - Prob. 60SYUCh. 9 - Prob. 61SYUCh. 9 - Prob. 62SYUCh. 9 - Prob. 63SYUCh. 9 - Prob. 64SYUCh. 9 - Prob. 65SYUCh. 9 - Prob. 66SYUCh. 9 - Prob. 67SYUCh. 9 - Prob. 68SYUCh. 9 - Prob. 69SYUCh. 9 - Prob. 70SYUCh. 9 - Prob. 1FOTCh. 9 - Prob. 2FOTCh. 9 - Prob. 3FOTCh. 9 - Prob. 4FOTCh. 9 - Prob. 5FOTCh. 9 - Prob. 6FOTCh. 9 - Prob. 7FOTCh. 9 - Prob. 8FOTCh. 9 - Prob. 9FOTCh. 9 - Prob. 10FOTCh. 9 - Prob. 11FOTCh. 9 - Prob. 12FOTCh. 9 - Prob. 13FOTCh. 9 - Prob. 14FOTCh. 9 - Prob. 15FOTCh. 9 - Prob. 16FOTCh. 9 - Prob. 17FOTCh. 9 - Prob. 18FOTCh. 9 - Prob. 19FOTCh. 9 - Prob. 20FOTCh. 9 - Prob. 21FOT
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