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hallow everyone

i am a tenth-grade student in Taiwan.What i want to know is that how to proove the curvature at point (a,(f(a))(assume f(x) is smooth at this point) is

f"(a)/(1+f'(a)^2)^(3/2))

i've thought this way:consider a circle first

in this circle the curvature at point P is lim arcPR/A as R approachs P ,curvature at point Q supposesd to be lim arcQR/(A-B) as R approachs Q

it might be d(arcQR)/d(A-B),equaling to d(arcQR)/d(A-(A-B)),because (A-B) is constant,it also equals to arcPR/A

So if we draw an ossculating cirsle at (a,(f(a)) ,we can reply the conclusion to deal with the problem,is this saying right??

i am a tenth-grade student in Taiwan.What i want to know is that how to proove the curvature at point (a,(f(a))(assume f(x) is smooth at this point) is

f"(a)/(1+f'(a)^2)^(3/2))

i've thought this way:consider a circle first

in this circle the curvature at point P is lim arcPR/A as R approachs P ,curvature at point Q supposesd to be lim arcQR/(A-B) as R approachs Q

it might be d(arcQR)/d(A-B),equaling to d(arcQR)/d(A-(A-B)),because (A-B) is constant,it also equals to arcPR/A

So if we draw an ossculating cirsle at (a,(f(a)) ,we can reply the conclusion to deal with the problem,is this saying right??

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