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$b>0$为常数,曲线$(\cos (t) \exp (-b t),\sin (t) \exp (-b t))$是一个对数螺线,其中参数$t$的取值范围是$(0,+\infty)$,则它的长度是有限的:$\underset{t_1\to \infty }{\text{lim}}\int_0^{t_1} \sqrt{(\cos (t) \exp (-b t)-b \sin (t) \exp (-b t))^2+(-\sin (t) \exp (-b t)-b \cos (t) \exp (-b t))^2} \, dt=\frac{\sqrt{b^2+1}}{b}$
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