- Let $f(x,y) = x^2y+3x$. Compute the differential $df$ and write it in the form $df = (\ )dx+(\ )dy$. Then write it as a matrix product.
- Let $\vec r(u,v) = (3u+2v, 4u^2, 2uv)$. Compute the differential $d\vec r$ and write it in the form $d\vec r = (\ )du+(\ )dv$. Then write it as a matrix product.
- Let $\vec F(x,y,z)=(-3x+2y, x-z,4x+3y+7z)$. Compute the differential $d\vec F$ and write it in the form $d\vec F = (\ )dx+(\ )dy+(\ )dz$. Then write it as a matrix product.
- For the function $\vec r(t) = (3\cos t, 3\sin t, t)$, Given an equation of the tantent line at $t=\pi/2$.
- For the function $\vec r(t) = (a\cos t, a\sin t, t)$, Given an equation of two tantent lines at $(a,t)=(3,\pi/2)$.
- Given an equation of the tangent plane to the surface from the previous problem at $(a,t)=(3,\pi/2)$.
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