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studyguide_2ndexam_MTH241_f11

# studyguide_2ndexam_MTH241_f11 - Study Guide for the 2nd...

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Study Guide for the 2nd Exam MTH241 Exam Date: 28th October 2011. In class Exam Covers Sections 14 . 1 - 14 . 8 You must know the followings 1. Domain of the function. 2. Limit and Continuity Prove or disprove the existance of limit. Do all the problems from the handout which I distributed in class 3. Partial Derivatives. Find f x ,f y ,f xx ,f yy ,f xy etc 4. Tangent plances and linearizations. Equation of the tangent plane of the curve z = f ( x,y ) at ( a,b ) is given by f x ( a,b )( x - a ) + f y ( a,b )( y - b ) - ( z - f ( a,b )) = 0 Linearization of f ( x,y ) = 0 around ( a,b ) is given by f x ( a,b )( x - a ) + f y ( a,b )( y - b ) - ( z - f ( a,b )) = 0. 5. Chain Rule. Must know z = f ( x,y ) ,x = g ( t ) ,y = h ( t ) dz dt = ∂f ∂x dx dt + ∂f ∂y dy dt z = f ( x,y ) ,x = g ( s,t ) ,y = h ( s,t ) dz ds = ∂f ∂x ∂x ∂s + ∂f ∂y ∂y ∂s dz dt = ∂f ∂x ∂x ∂t + ∂f ∂y ∂y ∂t Implicit Diﬀerentiation: F ( x,y ) = 0 ,y = f ( x ) dy dx = - F x F y 6. Directional Derivatives, Gradiant, Maximum rate of change. Finding the equations of

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studyguide_2ndexam_MTH241_f11 - Study Guide for the 2nd...

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