10. Show that 1/x, x are linearly independent on (0, 0).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Number 10 show all work
![EXERCISES 2.5
In each of Exercises 1-9, show that the given functions
are linearly independent on (-o, 0).
14. Suppose tha
are function
a) If f1, fa
(a, b), :
indeper
b) If f1, j
(c, d),
indepe
1. e3, e-2
2. cos 5x, sin 5x
3. e cos x, e2 sin x
4. e, xe
5. x? – 1, x? + 1, x +1
6. e", e2r, e3*
7. e, xe*, x²e*x
8. e, e* cos x, e sin x
9. x², \x]³
10. Show that 1/x, x are linearly independent on (0, ∞).
11. Show that x +1, x - 1, x are linearly dependent on
(-00, 00).
12. Show that sin² x, cos² x, cos 2x are linearly depen-
dent on (-00, o0).
15. a) Find t!
b) Show
w(
c) Show
linea
16. Use the
appropr
to find
e3x cos
13. Show that the two functions in Example 2 are lin-
early dependent on [0, o0).
functios
klan of f](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee22cf2f-b974-4b00-a3cf-09b388e7d65d%2Fb11499d0-8688-4a9c-a9ce-462f36a2a3fb%2Fz7lsgb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:EXERCISES 2.5
In each of Exercises 1-9, show that the given functions
are linearly independent on (-o, 0).
14. Suppose tha
are function
a) If f1, fa
(a, b), :
indeper
b) If f1, j
(c, d),
indepe
1. e3, e-2
2. cos 5x, sin 5x
3. e cos x, e2 sin x
4. e, xe
5. x? – 1, x? + 1, x +1
6. e", e2r, e3*
7. e, xe*, x²e*x
8. e, e* cos x, e sin x
9. x², \x]³
10. Show that 1/x, x are linearly independent on (0, ∞).
11. Show that x +1, x - 1, x are linearly dependent on
(-00, 00).
12. Show that sin² x, cos² x, cos 2x are linearly depen-
dent on (-00, o0).
15. a) Find t!
b) Show
w(
c) Show
linea
16. Use the
appropr
to find
e3x cos
13. Show that the two functions in Example 2 are lin-
early dependent on [0, o0).
functios
klan of f
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