MHB How to Find the Curvature of r(t)?

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SUMMARY

The curvature of the vector function r(t) = 9t i + 5 sin(t) j + 5 cos(t) k can be calculated using the formula for curvature in three-dimensional space. The first step involves finding the first derivative r'(t) and the second derivative r''(t). The curvature κ is then determined using the formula κ = |r'(t) × r''(t)| / |r'(t)|³. This discussion emphasizes the importance of showing work to facilitate assistance in solving the problem.

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Find the curvature. r(t) = 9t i + 5 sin(t) j + 5 cos(t) k
 
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