Calc III studyguide final PDF

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Download Calc III studyguide final PDF

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Study&guide:&& & Chapter&12:& & Section&12.1:&Distance&formula&and&equation&of&a&sphere.& Sample&problems: ,&18&

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& & & Section&12.2:&Vector&addition,&scalar&multiplication,&components,&magnitude,&definition&of&i,j,k.& Sample&problem:&#&21,&24.&

& Section&12.3:&Dot-product.&Definitions&and&properties,&angle&between&vectors,&projections,&perpendicular& vectors.& Sample&problems:
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& & Section&12.4:&Cross-product.&Definition&and&properties,&area&interpretation,&cross-product&with&(i,j,k),& triple&product&and&volume&interpretation,&coplanar&vectors.& Sample&problems:&#&13,&17,&27,&31,&35,&37.&&

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& & Section&12.5:&Equation&of&a&line&(vector,¶metric,&symmetric);&intersection&of&lines,¶llel&lines,&skew& lines& Equation&of&a&plane,&normal&to&a&plane,&intersection&of&planes,¶llel&planes,&distance&from&a&point&to&a& plane,&intersection&of&a&line&and&a&plane.& Sample&problems:,9,15,19,25,&27,30,&31,37,45,&51&(no&angle),&57,&65,&67,&71,&73&

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& & Chapter&13:& & Section&13.1:&Parametric&equations&of&space&curves& & Section&13.2:&Tangent&vector&to&a&curve&and&unit&tangent&vector&T& Sample&problems:&19,&20,&22&

& & Section&13.3:&Length,&arc&length,&reparametrization&by&arc&length,&curvature&(all&formulas&except&11),& normal&plane&& Sample&problems:&1,13,&25,&49&(only&normal&plane)& &

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& & Chapter&14:& & Section&14.1:&Domain&and&level&curves.& & Section&14.2:&Non-Existence&of&limits&using&trajectories,&definition&of&continuity,&squeeze&theorem&or&polar& coordinates& Sample&problems:&1,&15,&16,&17,&29,&37,&39,&41&

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& & & & Section&14.3:&Definition&of&partial&derivatives,&Clairaut’s&theorem& Sample&problems:&Any&problem&from&15&to&26,&Any&problem&from&53&till&62&

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& & Section&14.4:&Equation&of&tangent&plane&to&a&graph,&criteria&to&check&differentiability& Sample&problems:&1,3,5,&11,&13&(without&linearization)&

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Section&14.5:&Chain&rule& Sample&problems:&1,2,3,&7,11,&22,&24&

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& & Section&14.6:&Directional&derivatives--computational&rule,&definition&of&gradient,&maximizing&directional& derivatives,&equation&of&tangent&planes&to&level&surfaces,&normal&lines.& Sample&exercise:&7,11,&14,&22,25,&43&(a),&45&(a),&51.&

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& & Section&14.7:&Local&and&absolute&max&and&min,&critical&points,&second&derivatives&test,&saddle&points,& absolute&max&and&min&on&bounded&and&closed&sets& Sample&problems:&All&problems&from&5&to&20&(if&in&any&of&these&problems&D=0,&then&ignore&the&problem),& 34,&35,38&

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& & & Section&14.8:&Lagrange&multipliers&with&one&or&two&constraints& Sample&problems:&From&to&#&12.&From&#&17&to&#&20,,&from&31&to&41,-,.(b)&

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