- Solve the system of equations $3x-y+2z=4, 4x+z=7$. Start by picking one of the variables to equal $t$, and then solve for all the others in terms of $t$.
- Let $P(x)=ax^2+bx+c$. Let $f(x)=\ln(x+1)$. Solve the system of equations $P(0)=f(0) $, $P'(0)=f'(0) $, and $P' '(0)=f''(0) $ for the coefficients $a,b,c$.
- The volume of a box is $V=lwh$. Compute $dV$ in terms of $l, w,h, dl, dw, dh$. Then write your answer as the matrix product $$ dV = \begin{bmatrix}?&?&?\end{bmatrix}\begin{bmatrix}dl\\dw\\dh\end{bmatrix}.$$
- Find the distance between the two points $(3,5,-2)$ and $(-1,6,4)$.
- Give an equation of the sphere that passes through the point $(3,5,-2)$ and has the center $(-1,6,4)$.
- Find the component form of the vector that starts at $(4,-3)$ and ends at $(2,-2)$.
- Give a unit vector that points in the same direction as the previous. Then give a vector of length 3 that points in the same direction.
- Plot the vector valued function $\vec r(t) = (-2,1)t+(4,-3)$ for $0\leq t\leq 3$.
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