---## Determining Linear Independence of FunctionsDetermine whether the given set of functions is linearly independent on the interval \((-\infty, \infty)\).\[ f_1(x) = 6, \quad f_2(x) = \cos^2(x), \quad f_3(x) = \sin^2(x) \]- ○ Linearly dependent - ○ Linearly independent---In this exercise, you are asked to determine if the set of functions \( \{ f_1(x), f_2(x), f_3(x) \} \) are linearly independent over the interval \(( -\infty, \infty )\). Linear independence of functions implies that no function in the set can be written as a linear combination of the others.To explore more about linear independence of functions, you might want to review the Wronskian determinant and its application in checking independence for functions: [Link to relevant educational material on linear independence]. Ensure that you evaluate the provided functions properly by analyzing their structure and applying the necessary theoretical concepts to determine their linear dependence or independence.---

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Answered: Determine whether the given set of…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.CR: Chapter 6 Review

Problem 48CR

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Determine whether the given set of functions is linearly independent on the interval (-∞, ∞). f₁(x) = 6, f₂(x) = cos(x), f3(x) = sin²(x) O linearly dependent O linearly independent