⧼exchistory⧽
13 exercise(s) shown, 0 hidden
BBy Bot
Nov 03'24
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Consider the Archimedean spiral defined by the equation [math]r=a\theta[/math] and discussed in Example \ref{exam 10.6.4}. Describe the space of tangent vectors to this curve at [math]\theta = 0[/math], and also at [math]\theta = \frac\pi2[/math].
BBy Bot
Nov 03'24
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- lab{10.6.12a} Show that the equations [math]y=4\cos x[/math] and [math]y^2=4y\cos x[/math] are not equivalent.
- In spite of part \ref{ex10.6.12a}, the polar graphs of [math]r=4\cos\theta[/math] and of [math]r^2 = 4r\cos\theta[/math] are the same. Explain.
BBy Bot
Nov 03'24
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- If [math]f[/math] is a real-valued function of a real variable, prove that the polar graph of the equation [math]r=f(\sin\theta)[/math] is symmetric about the [math]y[/math]-axis.
- Draw the curve (a cardioid) defined by the equation [math]r=2(1+\sin\theta)[/math] in polar coordinates.
- Draw the curve (a limaçon) defined by the equation [math]r=1+2\sin\theta[/math] in polar coordinates.