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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.
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If \(x = t^3\) and \(y = 3t^5\), where \(t\) is any real number, what is the derivative of \(y\) with respect to \(x\) at \(x = 216\)?
Excel in math and science
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What is the equation of the tangent line to the curve \[x = 14 \sin t, y = 5\ \sin(t + \sin t) \] at \((0,0)\)?
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If \(x = \ln t\) and \(y = 3 t^3 + 9 \ln t\) what is \(\displaystyle{\frac{d y}{d x}}?\)
Excel in math and science
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If \(x=t+\frac{1}{t}\) and \(y=t^2+\frac{1}{t^2}\), what is the derivative of \(y\) with respect to \(x\) at \(x=21\)?
Excel in math and science
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At time \(t\), the coordinates of a point \(P\) are given by \( (4 \cos t, 2 \sin t) \). At time \(t=\frac{\pi}{4}\), the magnitudes of velocity and acceleration are \(m\) and \(n\), respectively. What is \(m^2+n^2\)?
Excel in math and science
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by Brilliant Staff