Let S = {(λ, μ) ∈ R × R: f(t) = (|λ| e^(|t|) − μ) · sin(2|t|), t ∈ R, is a differentiable function}. Then S is a subset of

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R × [0, ∞). The correct option is R × [0, ∞) because for the function f(t) to be differentiable, the term |λ| e^(|t|) must be non-negative, which requires λ to be any real number and μ to be non-negative, thus forming the set of all pairs (λ, μ) where μ is in [0, ∞).

Let S = {(λ, μ) ∈ R × R: f(t) = (|λ| e^(|t|) − μ) · sin(2|t|), t ∈ R, is a differentiable function}. Then S is a subset of

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