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? ? ? 1. f(t) = 4t² + 28t, g(t) = 4t² - 28t 2. f(0) cos(30), = g(0) = -8 cos³ (0) + 6 cos (0) 3. f(t) = 3t, g(t) = |t| 4. f(t) = et cos(ut), g(t) = et sin(ut), μ‡0

? ? ? 1. f(t) = 4t² + 28t, g(t) = 4t² - 28t 2. f(0) cos(30), = g(0) = -8 cos³ (0) + 6 cos (0) 3. f(t) = 3t, g(t) = |t| 4. f(t) = et cos(ut), g(t) = et sin(ut), μ‡0

Advanced Engineering Mathematics
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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Determine which of the following pairs of functions are linearly independent

1. \( f(t) = 4t^2 + 28t \), \quad \( g(t) = 4t^2 - 28t \) 2. \( f(\theta) = \cos(3\theta) \), \quad \( g(\theta) = -8\cos^3(\theta) + 6\cos(\theta) \) 3. \( f(t) = 3t \), \quad \( g(t) = |t| \) 4. \( f(t) = e^{\lambda t} \cos(\mu t) \), \quad \( g(t) = e^{\lambda t} \sin(\mu t) \), \quad \( \mu \neq 0 \)
Transcribed Image Text:1. \( f(t) = 4t^2 + 28t \), \quad \( g(t) = 4t^2 - 28t \) 2. \( f(\theta) = \cos(3\theta) \), \quad \( g(\theta) = -8\cos^3(\theta) + 6\cos(\theta) \) 3. \( f(t) = 3t \), \quad \( g(t) = |t| \) 4. \( f(t) = e^{\lambda t} \cos(\mu t) \), \quad \( g(t) = e^{\lambda t} \sin(\mu t) \), \quad \( \mu \neq 0 \)
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