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Sagot :
The equation for curvature is given by κ = |r' × r''|/|r'|3 where r' = dr/dt and r'' = d2r/dt2. the curvature of r(t) at the point (7,1,1), r(t)=<7t,t2,t3> is √14/√490.
The equation for curvature is given by κ = |r' × r''|/|r'|3 where r' = dr/dt and r'' = d2r/dt2.
We are given the point (7,1,1) which is the same as t=1.
Therefore, we can substitute t=1 into the function r(t) to obtain r(1) =<7,1,1>.
From this, we can calculate the derivatives r' and r'' of the function r(t) at the point (7,1,1).
r' = <7,2,3>
r'' = <0,2,6>
Then, we can calculate the curvature κ using the equation κ = |r' × r''|/|r'|3.
κ = |<7,2,3> × <0,2,6>|/|<7,2,3>|3
= |<0,-14,18>|/|<7,2,3>|3
= √14/√490
Learn more about equations for curvature here
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