Question

Find the radius of curvature for y=e^x at x=1.

Answer 1

\[k(x)=\frac{ \left| y'' \right| }{ [1+(y')^2]^{3/2} }\]

Answer 2

\[k(x)=\frac{ e^x }{ (e ^{2x}+1)^{3/2} }\]

Answer 3

^ That above is the curvature, so how do I find the radius of curvature at x=1?

Answer 4

plug in 1

Answer 5

normally, radius of curvature is 1/k

Answer 6

So I got \[k(1)=\frac{ e }{ (e^2+1)^{3/2} }\]

Answer 7

http://mathworld.wolfram.com/RadiusofCurvature.html this site says it should be the reciprocal of that

Answer 8

which I think that @IrishBoy123 said what he said above

Answer 9

why I think*

Answer 10

So I got \[R=\frac{ (e^2+1)^{3/2} }{ e }\]

Answer 11

that sounds great to me :)

Answer 12

Thank you so much, @myininaya !