Homework Soursefind the curvature and the radius of curvature of the curve
find the curvature and the radius of curvature of the curve y=ln(4x-3) at the point P(1,0)
Solution
The curve can be parameterized r=(x,y,0) v=(1,y\',0) a=(0,y\'\',0) v x a=(0,0,y\'\') The curvature is then k=|v x a|/|v|^3=|y\'\'|/(1+(y\')^2)^(3/2) y\'=4/(4x-3) y\'\'=-16/(4x-3)^2 when x=0 we have y\'=-4/3 y\'\'==16/9 k=(16/9)/(1+16/9)^(3/2) =(16/9)/(5/3)^3 =16/9*27/125 =48/125 The radius of curvature is 1/k=125/48
