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→Challenging Problems
'''2.''' Prove that the geometric definition of <math>\vec{a}\times\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.
'''3.''' Suppose <math>f(x,y)</math> has continuous derivatives of all orders. Prove <math>\partial_{xy}f = \partial_{yx}f</math>.
'''3.''' Suppose <math>f(x,y)</math> has continuous derivatives of all orders. Prove <math>\partial_{xy}f = \partial_{yx}f</math>.
{{MVCalc}}