25. sinx, csc x; (0, π)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 31E
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In Problems 23-28 show by computing the Wronskian that the given functions are linearly independent on the indicated interval.
SECTION 4.1 Preliminary Theory
131
25. sinx, csc x; (0, π)
26. tan x, cot x; (0, π/2)
27. e, ex, ex,
(-∞0,00)
28. x, x ln x, x² In x; (0, ∞)
29. Observe that for the functions f₁(x) = 2 and f₂(x) = e*,
1. fi(0)-2f₂(0) = 0.
Does this imply that f₁ and f₂ are linearly dependent on any interval
containing x = 0?
Transcribed Image Text:SECTION 4.1 Preliminary Theory 131 25. sinx, csc x; (0, π) 26. tan x, cot x; (0, π/2) 27. e, ex, ex, (-∞0,00) 28. x, x ln x, x² In x; (0, ∞) 29. Observe that for the functions f₁(x) = 2 and f₂(x) = e*, 1. fi(0)-2f₂(0) = 0. Does this imply that f₁ and f₂ are linearly dependent on any interval containing x = 0?
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