Let S=(λ,μ)∈R×R and
f(t)=(∣λ∣e∣t∣−μ).sin2∣t∣
RHD=h→0limhf(0+h)−0=h→0lim(∣λ∣eh−μ)hsin2h=2(∣λ∣−μ)
LHD=h→0lim−hf(0−h)−0=h→0lim(∣λ∣eh−μ)−hsin2h=−2(∣λ∣−μ)
Now, LHD=RHD if ∣λ∣=μ
⇒μ≥0 and λ∈R
Let S={(\lambda ,\mu )\in R\times R :f(t)=(|\lambda |{e}^{|t|}-\mu )\mathrm{sin}(2|t|),t\in R is a differential function}. Then, S is a subset of :
Held on 15 Apr 2018 · Verified 6 Jul 2026.
(−∞,0)×R
R×[0,∞)
[0,∞)×R
R×(−∞,0)
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