Final_exam_practice

Final_exam_practice - MATH 2401 December 10, 2009 Sections...

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Unformatted text preview: MATH 2401 December 10, 2009 Sections F4 & F5 11:30-14:20 PRACTICE FINAL EXAM Name: gtID # : Note: There are eight problems in this exam, each worth 20 points. Write out your solutions neatly and explain your work. Calculators are not allowed. Problem number Points 1 2 3 4 5 6 7 8 Total: Basic formulas: Unit tangent and principal normal: T ( t ) = r ( t ) k r ( t ) k , N ( t ) = T ( t ) k T ( t ) k Arc length: L ( C ) = Z b a k r ( t ) k dt Curvature: = d T ds = k d T /dt k ds/dt = k v a k k v k 3 = | x ( t ) y 00 ( t )- y ( t ) x 00 ( t ) | [[ x ( t )] 2 + [ y ( t )] 2 )] 3 / 2 Components of acceleration: a = a T T + a N N a T = d 2 s dt 2 = T a = v a k v k a N = ds dt 2 k T a k = k v a k k v k Gradient: f ( x ) = f x ( x ) i + f y ( x ) j + f z ( x ) k Directional derivative: f u ( x ) = f ( x ) u Chain rule: d dt [ f ( r ( t ))] = f ( r ( t )) r ( t ) The second-partials test: A = 2 f x 2 , B = 2 f yx , C =...
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Final_exam_practice - MATH 2401 December 10, 2009 Sections...

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