math 212 multivariable calculus final exam instructions you have 3 hours to complete the exam 12 problems this is a closed book closed notes exam use of calculators is not ...
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...Math multivariable calculus final exam instructions you have hours to complete the problems this is a closed book notes use of calculators not permitted show all your work for full credit please do forget write name and instructor s on blue cover too print upon nishing sign pledge below onmyhonor i neither given nor received any aid signature problem max points score total find equation tangent line path c t cost sint at solution derivative by sin cos point l or may let f r be dened x y z ex set heads unit vectors v in such that increases its maximum rate change direction starting from which determine hint circle gradient xexp yexp so vector greatest increase function calculate maximimum evaluating directional df just goal nd dfv now applying constraint nal equations are absolute minimum disk d interior if critical but hence has extrema we lagarange multiplier g solve simultaneously then thus therefore maxima simple curve parametrization curvature ds compute rcos rsin note length ellip...