Hi,
I need to find the curvature k of y=sqrt(R^2 - x^2)
I know k = |f''| / (1 + f' ^2) ^1.5
But I think I have gone somewhere with my differentiation as I didn't end up with k = 1/R which is the answer :/
Thanks in advance for the help.
Hi,
I need to find the curvature k of y=sqrt(R^2 - x^2)
I know k = |f''| / (1 + f' ^2) ^1.5
But I think I have gone somewhere with my differentiation as I didn't end up with k = 1/R which is the answer :/
Thanks in advance for the help.
$\displaystyle y' = -\frac{x}{y}$
quotient rule ...
$\displaystyle y'' = -\frac{y - xy'}{y^2}$
$\displaystyle y'' = -\frac{y - x\left(-\frac{x}{y}\right)}{y^2}$
$\displaystyle y'' = -\frac{y + \frac{x^2}{y}}{y^2}$
multiply numerator and denominator by $\displaystyle y$ to clear the complex fraction ...
$\displaystyle y'' = -\frac{y^2 + x^2}{y^3}$
$\displaystyle y'' = -\frac{R^2}{y^3}$