radius of curvature

find the radius of curvature of y = exp(-x) at x =1

y' = -exp(-x)

y" = exp(-x)

at x = 1

y' = -exp(-1)= -1 /e

y" = exp(-1) = 1/e

radius of curvature = { [ 1 + (y')² ] ^(3/2) } / y"

radius of curvature = { [e² + 1] ^(3/2) } / e²

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