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 :

Step-by-step solution

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