# 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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