Question
If Δ(x) = ∣∣
∣
∣∣xnsin xcos xn!sinnπ2cosnπ2aa2a3∣∣
∣
∣∣, then the value of dndxn[Δ(x)] at x=0 is
∣
∣∣xnsin xcos xn!sinnπ2cosnπ2aa2a3∣∣
∣
∣∣, then the value of dndxn[Δ(x)] at x=0 is
Answer: Option B
:
B
dndxn[Δ(x)]=∣∣
∣
∣
∣∣dndxnxndndxnsinxdndxncosxn!sin(nπ2)cos(nπ2)aa2a3∣∣
∣
∣
∣∣=∣∣
∣
∣
∣∣n!sin(x+nπ2)cos(x+nπ2)n!sin(nπ2)cos(nπ2)aa2a3∣∣
∣
∣
∣∣⇒[Δn(x)]x=0=∣∣
∣
∣
∣∣n!sin(0+nπ2)cos(0+nπ2)n!sin(nπ2)cos(nπ2)aa2a3∣∣
∣
∣
∣∣=01SinceR1≡R2}.
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:
B
dndxn[Δ(x)]=∣∣
∣
∣
∣∣dndxnxndndxnsinxdndxncosxn!sin(nπ2)cos(nπ2)aa2a3∣∣
∣
∣
∣∣=∣∣
∣
∣
∣∣n!sin(x+nπ2)cos(x+nπ2)n!sin(nπ2)cos(nπ2)aa2a3∣∣
∣
∣
∣∣⇒[Δn(x)]x=0=∣∣
∣
∣
∣∣n!sin(0+nπ2)cos(0+nπ2)n!sin(nπ2)cos(nπ2)aa2a3∣∣
∣
∣
∣∣=01SinceR1≡R2}.
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