Without the aid of the Wronskian, determine whether the given set of functions is linearly independent or linearly dependent on the indicated interval.

(a) f₁(x) = ln x, f₂(x) = ln x², (0, ∞)

(b) f₁(x) = xⁿ, f₂(x) = xⁿ⁺¹, n = 1, 2, . . . , (-∞, ∞)

(c) f₁(x) = x, f₂(x) = x + 1, (-∞, ∞)

(d)

(e) f₁(x) = 0, f₂(x) = x, (-5, 5)

(f) f₁(x) = 2, f₂(x) = 2x, (-∞, ∞)

(g) f₁(x) = x², f₂(x) = 1 - x², f₃(x) = 2 + x², (-∞, ∞)

(h) f₁(x) = xe^x+1, f₂(x) = (4x - 5)e^x, f₃(x) = xe^x, (-∞, ∞)

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1. f,(x) = sin x, (-0, ) %3D fi(x) = cos x +