Q) Find the domain of 𝑝(𝑥)=sin^(−1) (1−2𝑥^2 ). Hence,find the value of 𝑥 for which p(𝑥)=𝜋/6.

Q) If 2cos^(−1) 𝑥 = 𝑦,then(A) 0≤𝑦≤𝜋(B) −𝜋≤𝑦≤𝜋(C) 0≤𝑦≤2𝜋(D) −𝜋≤𝐲 ≤ 0 #shivangmathsacademy

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Control systems exercise: find the percent overshoot of the system with the given transfer function. A second-order system doesn’t always settle smoothly. In many real-world systems, the output temporarily exceeds its final value before settling — a phenomenon known as percent overshoot. Why does this matter? Because overshoot isn’t just a mathematical quantity. In practical applications, excessive overshoot can lead to mechanical stress, voltage spikes, temperature excursions, or reduced passen

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