Use the theorem given below to find the curvature of r(t)=t7j+t5k. Theorem: The curvature of the curve given by the vec

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Use The Theorem Given Below To Find The Curvature Of R T T7j T5k Theorem The Curvature Of The Curve Given By The Vec 1 (33.72 KiB) Viewed 38 times

Use the theorem given below to find the curvature of r(t)=t7j+t5k.  Theorem: The curvature of the curve given by the vector function r is κ(t)=∣r′(t)∣3∣r′(t)×r′′(t)∣​. κ(t)=(49t11+25t9)(23​)35t9​​
Consider the following. r(t)=⟨4t2,ln(t),tln(t)⟩ Find r′(t) and r′′(t) r′(t)=<8t,t1​,ln(t)+1> r′′(t)=<8,−t21​,t1​> Find the curvature of r(t)=⟨4t2,ln(t),tln(t)⟩ at the point (4,0,0).
Find the vectors T,N, and B at the given point. r(t)=⟨t2,32​t3,t⟩,(1,−32​,−1)T=<−32​,32​,31​>N=<−31​,−32​,32​>​