Calculus and Geometry go Hand in Hand

Calculus Level 5

The circle \(x^{2}+y^{2}=1\) cuts the \(x\)-axis at \(P\) and \(Q\) .Another circle with centre at Q and having a variable radius intersects the first circle at \(R\) , above the \(x\)-axis and the line segment \(PQ\) at \(S\) .

Find the maximum possible area of \(\Delta QSR\) .

Let the area which comes out be \(\frac{1}{k}\) .

Evaluate , \[\sum_{r=0}^{\infty} \dfrac{8\cdot k}{ (2r+1)^{2} \pi^{2} – (2 k)^{2}}\]

Report the answer correct up to 3 places of decimals .

HINT : Whenever Trigonometry is involved, we should use radians .


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