{dx^2}\) as a function of \(t\text{,}\) without simplifying your answer. Sketch the curve \begin{equation*} x=\sin ^2\pi t, \ y=\cos ^2 \pi t, \ 0\leq t\leq 2\text{.} \end{equation*} Clearly label the ...

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An object is moving counter-clockwise along a circle with the centre at the origin. At \(t=0\) the object is at point \(A(0,5)\) and at \(t=2\pi\) it is back to point \(A\) for the first time.