iii. On the same plot sketch graphs of the functions f(x) and x² for 0 ≤ x ≤ 3. ii. Find the coefficients a1, a2, a3 for the best in the mean approximation of x² on the interval [0,3]. 3 f(x) = Σ akok (x) k=1 4. (a) Let the inner product of piecewise continuous functions on the interval 0 ≤ x ≤ 3 be given by 3 (f, 9) = fr³ f(x)9(x) dr. Consider three piecewise constant functions 01(x), 02(x) and 03(x): (х) ¢k(x) = { } 1, - if k − 1 < x < k k = 1, 2, 3. 0, at all other points, i. Show that 1(x), 2(x), 03(x) form an orthonormal system of functions.
iii. On the same plot sketch graphs of the functions f(x) and x² for 0 ≤ x ≤ 3. ii. Find the coefficients a1, a2, a3 for the best in the mean approximation of x² on the interval [0,3]. 3 f(x) = Σ akok (x) k=1 4. (a) Let the inner product of piecewise continuous functions on the interval 0 ≤ x ≤ 3 be given by 3 (f, 9) = fr³ f(x)9(x) dr. Consider three piecewise constant functions 01(x), 02(x) and 03(x): (х) ¢k(x) = { } 1, - if k − 1 < x < k k = 1, 2, 3. 0, at all other points, i. Show that 1(x), 2(x), 03(x) form an orthonormal system of functions.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
Related questions
Question
![iii. On the same plot sketch graphs of the functions f(x) and x² for 0 ≤ x ≤ 3.
ii. Find the coefficients a1, a2, a3 for the best in the mean approximation
of x² on the interval [0,3].
3
f(x) = Σ akok (x)
k=1
4. (a) Let the inner product of piecewise continuous functions on the interval 0 ≤ x ≤ 3
be given by
3
(f, 9) = fr³ f(x)9(x) dr.
Consider three piecewise constant functions 01(x), 02(x) and 03(x):
(х)
¢k(x) = { }
1,
-
if k − 1 < x < k
k = 1, 2, 3.
0,
at all other points,
i. Show that 1(x), 2(x), 03(x) form an orthonormal system of functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc05cf68-81ae-4970-8864-261fc4d70f9c%2F15ffbd27-0645-40aa-9537-0ff6d193faa4%2F2tjhsi8_processed.png&w=3840&q=75)
Transcribed Image Text:iii. On the same plot sketch graphs of the functions f(x) and x² for 0 ≤ x ≤ 3.
ii. Find the coefficients a1, a2, a3 for the best in the mean approximation
of x² on the interval [0,3].
3
f(x) = Σ akok (x)
k=1
4. (a) Let the inner product of piecewise continuous functions on the interval 0 ≤ x ≤ 3
be given by
3
(f, 9) = fr³ f(x)9(x) dr.
Consider three piecewise constant functions 01(x), 02(x) and 03(x):
(х)
¢k(x) = { }
1,
-
if k − 1 < x < k
k = 1, 2, 3.
0,
at all other points,
i. Show that 1(x), 2(x), 03(x) form an orthonormal system of functions.
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