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- Title: MATH_200_spring_07_exam_3_with_solutions
- Type: Notes
- School: Drexel
- Course: MATH 200
- Term: Spring
Coursehero >> Pennsylvania >> Drexel >> MATH 200
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> CALC >> 200 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> CALC >> 200 Spring, 2008
Path: Drexel >> CALC >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> CALC >> 200 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> CALC >> 200 Spring, 2008
Path: Drexel >> CALC >> 200 Spring, 2008
Path: Drexel >> CALC >> 200 Spring, 2008
Path: Drexel >> CALC >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> MATH >> 200 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> COOP >> 101 Spring, 2008
Path: Drexel >> COOP >> 101 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Drexel >> PHYS >> 102 Spring, 2008
Path: Michigan State University >> MMG >> 409 Summer, 2008
Path: Michigan State University >> MMG >> 409 Summer, 2008
Path: Michigan State University >> MMG >> 409 Summer, 2008
Path: Michigan State University >> MMG >> 409 Summer, 2008
Path: Michigan State University >> MMG >> 409 Summer, 2008
Path: UNC >> EXSS >> 380 Summer, 2008
Path: UNC >> EXSS >> 380 Summer, 2008
Path: UCSD >> MAE >> 143B Spring, 2007
Path: UCSD >> MAE >> 143B Spring, 2007
Path: UCSD >> MAE >> 143B Spring, 2007
Path: UCSD >> MAE >> 143B Spring, 2007
Path: UCSD >> MAE >> 143B Spring, 2007
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Three Exam MATH 200 Spring, 2007 Name_______________________________ Section____________ Show all your work on the exam paper, legibly and in detail, to receive full credit. No Calculators. Page 1) _ 2) _ 3) _ 4) _ 5) _ 6) _ Total 1. (20 points) Use the appropriate form of the multi-dimensional chain rule (MDCR) to find z t and z s . You must use the MDCR to obtain full credit. 2 1 z e x y ; x st , y s Page 1 of 6 2. (20 points) Find a unit vector in the direction in which f x, y 4 x 3 y 2 increases most rapidly at P 1, 1 , and find the rate of change of f at P in that direction. Page 2 of 6 3. (20 points) Find an equations for the tangent plane and parametric equations for the normal line to the line to the surface e z 3 y sin 3 x at the point P 6 , 0,1 . Page 3 of 6 4. (20 points) Locate all relative maxima, relative minima, and saddle points, if any. f x, y y 2 xy 3 y 2 x 3 Page 4 of 6 5. (5 points) Find the normal vector for the paraboloid z point (1, -1, 2). x2 y 2 at the (5 points) Find the normal vector for the ellipsoid x 2 point (1, -1, 2). 4y2 z2 9 at the (10 points) Find the parametric equations for the tangent line of the curve of intersection of the paraboloid z x 2 y 2 and the ellipsoid x 2 4 y 2 z 2 9 at the point (1, -1, 2). Page 5 of 6 6. (10 points) Consider the following modification of problem 1: 2 1 z ex y ; x st , y . Find z t and z s WITHOUT using the chain rule. s Page 6 of 6
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Description: ...
CH09_HOPath: Michigan State University >> MMG >> 409 Summer, 2008
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CH10_HOPath: Michigan State University >> MMG >> 409 Summer, 2008
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CH11_HOPath: Michigan State University >> MMG >> 409 Summer, 2008
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CH07_HOPath: Michigan State University >> MMG >> 409 Summer, 2008
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neuro2Path: UNC >> EXSS >> 380 Summer, 2008
Description: Loop Systems Open Loop (Feedback) -Sensory input processed to generate movement commands. -CNS changes output based on sensory input. Closed Loop (Feedforward) -CNS provides output independent of sensory input or movement outcomes -Must have knowled...
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Description: Tenomuscular Receptors Muscle spindle -Sensitive to muscle length and muscle length -Indirect indication of joint position sense and kinesthesia -Efferent innervations by gamma and beta motorneurons. Golgi Tendon Organ -Sensitive to muscle tension -...
midterm06-springPath: UCSD >> MAE >> 143B Spring, 2007
Description: ...
midterm05-sum-solutionPath: UCSD >> MAE >> 143B Spring, 2007
Description: MAE 143B Linear Control Prof. M. Krstic August 15, 2005 MIDTERM NAME: Solution Open books and notes. Present your reasoning and calculations clearly. Random or inconsistent etchings will not be graded. Write only on the paper provided. If you...
mae143b_midterm_sum2_06Path: UCSD >> MAE >> 143B Spring, 2007
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