Question

Find the radius of curvature at y=log x / x at x =1

Answer 1

Step-by-step explanation:

TAKE 1ST DERIVATIVE AND THEN 2ND DERIVATIVE AND INSERT IT IN THE FORMULA

Answer 2

Answer:

$radius \: \: of \: \: curvature \: = \frac{ ({1 + ( { \frac{dy}{dx}) }^{2} )}^{ \frac{3}{2} } }{ \frac{ {d}^{2} y}{ {dx}^{2} } }$

$\frac{dy}{dx} = \frac{1 - log_{}(x) }{ {x}^{2} } \\ \\ at \: \: x = 1 \\ \\ \frac{dy}{dx} = 1 \\ \\ = > \frac{ {d}^{2} y}{ {dx}^{2} } = \frac{2 log(x) - 3}{ {x}^{3} } \\ \\ at \: \: x = 1 \\ \\ \frac{ {d}^{2} y}{ {dx}^{2} } = - 3$

$so \: \: radius \: \: of \: \: curvature \: = \frac{ {(1 + 1)}^{ \frac{3}{2} } }{ 3} \\ \\ = \frac{ {2}^{ \frac{3}{2} } }{ 3}$

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