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Calculus

Calculus of Parametric Equations

Parametric Equations - Tangent

         

Consider the polar curve \( r\theta = 6 \). What is the slope of the tangent line of the polar curve at \( \theta = \pi \)?

Given the curve \[x=1-2t, y=5-4t+2t^2,\] what is the equation of the tangent line to the curve at \(x=5 ?\)

For the curve given by \[x=\frac{9t}{1+t^2}, y=\frac{1-t^2}{1+t^2},\] what is the equation of the tangent line to the curve for \(t=2 ?\)

Consider the polar curve \( r = 22 \sin \theta \). What is the slope of the tangent line at \( \theta = \frac{\pi}{6} \)?

A curve is defined by \((x,y) =\left(\cos^3 \theta, \sin^3 \theta \right)\). If the equation for the tangent line at \(\theta=\frac{2}{3}\pi\) is \(y=ax+b\), what is the value of \( a \times b \)?

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