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'''3.''' Let <math>\vec{F}(r,\theta,\phi) = (-r^{-1})(\vec{i}+\vec{j}+\vec{k})</math>. Describe <math>\vec{F}</math> in words. Find a formula for <math>\vec{F}</math> in Cartesian coordinates.
'''3.''' Let <math>\vec{F}(r,\theta,\phi) = (-r^{-1})(\vec{i}+\vec{j}+\vec{k})</math>. Describe <math>\vec{F}</math> in words. Find a formula for <math>\vec{F}</math> in Cartesian coordinates.
'''4.''' Find the partial derivatives <math>\frac{\partial}{\partial x}</math> and <math>\frac{\partial}{\partial y}</math> of <math> 3e^{x-y}\sin(y)+2x</math>
'''5.''' Find the partial derivatives <math>\partial_x, \partial_y</math> and <math>\partial_z</math> of <math>\frac{x}{y+z} + \frac{y}{x+z}</math>.
==Challenging Problems==
==Challenging Problems==
'''1.''' Prove that the geometric definition of <math>\vec{a}\cdot\vec{b}</math> matches our coordinate expression.
'''2.''' Prove that the geometric definition of <math>\vec{a}\times\vec{b}</math> matches our coordinate expression.
{{MVCalc}}
{{MVCalc}}