For the cartesian curve y=f(x) with ‘s’ as arc length which of the following condition holds good?
Posted: Thu Jul 14, 2022 9:29 am
a) \(\frac{ds}{dx} = \sqrt{1+(\frac{dy}{dx})^2}\)
b) \(\frac{d^2s}{dx^2} = \sqrt{1-(\frac{dy}{dx})^2}\)
c) \(\frac{dy}{dx} = \sqrt{1+(\frac{ds}{dx})^2}\)
d) \(\sqrt{(\frac{ds}{dx})^2 + (\frac{dy}{dx})^2} = 1\)
b) \(\frac{d^2s}{dx^2} = \sqrt{1-(\frac{dy}{dx})^2}\)
c) \(\frac{dy}{dx} = \sqrt{1+(\frac{ds}{dx})^2}\)
d) \(\sqrt{(\frac{ds}{dx})^2 + (\frac{dy}{dx})^2} = 1\)