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In Problems 1 through 6, show directly that the given functions are linearly dependent on the real line. That is, find a non- trivial linear combination of the given functions that vanishes identically. 1. f(x) = = 5x – 8x² 2. f(x) = 5, g(x) = 2 – 3x², h(x) = 10 + 15x² 3. f(x) = 0, g(x) = sin x, h(x) = e* 4. f(x) = 17, g(x) = 2 sin² x, h(x) = 3 cos² x 5. f(x) = 17, g(x) = cos² x, h(x) : 6. f(x) = e*, g(x) = cosh x, h(x) = sinh x 2.x, g(x) = 3x², h(x) - || - = cos 2x

In Problems 1 through 6, show directly that the given functions are linearly dependent on the real line. That is, find a non- trivial linear combination of the given functions that vanishes identically. 1. f(x) = = 5x – 8x² 2. f(x) = 5, g(x) = 2 – 3x², h(x) = 10 + 15x² 3. f(x) = 0, g(x) = sin x, h(x) = e* 4. f(x) = 17, g(x) = 2 sin² x, h(x) = 3 cos² x 5. f(x) = 17, g(x) = cos² x, h(x) : 6. f(x) = e*, g(x) = cosh x, h(x) = sinh x 2.x, g(x) = 3x², h(x) - || - = cos 2x

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.9: Combining Functions
Problem 50HP
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Differential Equations

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In Problems 1 through 6, show directly that the given functions are linearly dependent on the real line. That is, find a non- trivial linear combination of the given functions that vanishes identically. 1. f(x) = = 5x – 8x² 2. f(x) = 5, g(x) = 2 – 3x², h(x) = 10 + 15x² 3. f(x) = 0, g(x) = sin x, h(x) = e* 4. f(x) = 17, g(x) = 2 sin² x, h(x) = 3 cos² x 5. f(x) = 17, g(x) = cos² x, h(x) : 6. f(x) = e*, g(x) = cosh x, h(x) = sinh x 2.x, g(x) = 3x², h(x) - || - = cos 2x
Transcribed Image Text:In Problems 1 through 6, show directly that the given functions are linearly dependent on the real line. That is, find a non- trivial linear combination of the given functions that vanishes identically. 1. f(x) = = 5x – 8x² 2. f(x) = 5, g(x) = 2 – 3x², h(x) = 10 + 15x² 3. f(x) = 0, g(x) = sin x, h(x) = e* 4. f(x) = 17, g(x) = 2 sin² x, h(x) = 3 cos² x 5. f(x) = 17, g(x) = cos² x, h(x) : 6. f(x) = e*, g(x) = cosh x, h(x) = sinh x 2.x, g(x) = 3x², h(x) - || - = cos 2x
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