Matematika/Lanko ilgis: Skirtumas tarp puslapio versijų
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46 eilutė:
:<math>\frac{dy}{dx}=\frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}.</math>
:<math>\frac{dx}{d\theta}=\frac{d\rho}{d\theta}\cos\theta-\rho\sin\theta, \quad \frac{dy}{d\theta}=\frac{d\rho}{d\theta}\sin\theta+\rho\cos\theta.</math>
:<math>dx=(\frac{d\rho}{d\theta}\cos\theta-\rho\sin\theta)d\theta.</math>
:<math>ds=\sqrt{1+\left(\frac{dy}{dx}\right)^2} dx =\sqrt{1+\left(\frac{\frac{d\rho}{d\theta}\sin\theta+\rho\cos\theta}{\frac{d\rho}{d\theta}\cos\theta-\rho\sin\theta}\right)^2} (\frac{d\rho}{d\theta}\cos\theta-\rho\sin\theta)d\theta =</math>
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