Let S = { λ , μ ∈ R × R : f t = λ e t - μ sin ⁡ 2 t , t ∈ R is a differential function}. Then, S is a subset of :

Question

Let S = { λ , μ ∈ R × R : f t = λ e t - μ sin ⁡ 2 t , t ∈ R is a differential function}. Then, S is a subset of :, - ∞ , 0 × R, R × 0 , ∞ ), 0 , ∞ ) × R, R × - ∞ , 0

MARKS App · Accepted Answer

Let S = λ , μ ∈ R × R and f t = λ e t - μ . sin ⁡ 2 t R H D = lim h → 0 ⁡ f 0 + h - 0 h = lim h → 0 ⁡ λ e h - μ sin 2 ⁡ h h = 2 ( λ - μ ) L H D = lim h → 0 ⁡ f 0 - h - 0 - h = lim h → 0 ⁡ λ e h - μ sin 2 ⁡ h - h = - 2 ( λ - μ ) Now, L H D = R H D if λ = μ ⇒ μ ≥ 0 and λ ∈ R

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