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Calculus of Parametric Equations
Parametric equations can be quite handy, and we don't want to unravel them just to do Calculus. Some tricks can bend traditional derivative and integral methods to apply to parametric equations.
If \(y\) is a function of \(x\) as defined by the parametric relation \(y=3\sin ^{ 2 }{ t }\) when \(x=\tan { t } \), then determine the value of \(\displaystyle\lim_{ x\rightarrow \infty }{ y }\) .
by
Yagna Patel
\[\large x = a(t - \sin t) \\ \large y = a(1 - \cos t)\]
What is the area of the region bounded by the two arcs of the cycloid in the above figure?
by
Akhil Bansal
What is the length of the arc of the curve \(x^{\frac{2}{3}} + y^{\frac{2}{3}}=4\)?
by
Lokeshwar Tabjula
The area enclosed by the 2 cute adorable little fine loops is equals to \( \frac {a}{b} \) for coprime positive integers \(a\) and \(b\). What is the value of \(a+b\)?
by
Pi Han Goh
The location of a dot \(P\) at a given time \(t\) in the \(xy\) plane is given by \((x,y) = (t - \sin t, 1 - \cos t)\). What is the distance traveled by \(P\) in the interval \(0 \leq t \leq 2\pi\)?
by
Arron Kau