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Multivariable & Vectorhard
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Compute the surface area element dSdSdS for the parametric surface r⃗(u,v)=(ucos⁡v,usin⁡v,2u)\vec{r}(u,v) = (u \cos v, u \sin v, 2u)r(u,v)=(ucosv,usinv,2u) where 0≤u≤2,0≤v≤2π0 \le u \le 2, 0 \le v \le 2\pi0≤u≤2,0≤v≤2π (a cone). What is dSdSdS?