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studyguide 4 mth - Study Guide for the 4th Exam MTH241 Exam...

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Study Guide for the 4th Exam MTH241 Exam Date: 9th December 2011. In class Exam Covers Sections 16 . 1 16 . 6 You must know the followings 1. Line integral and line integral in space. 2. Fundamental theorem of line integrals and independent of path. 3. Green’s Theorem 4. Calculate Work Done. 5. Divergence ( . F ) and Curl ( ∇ × F ) 6. Conservative Field. 7. Parametric Surfaces and their areas, equation of tangent plane. Sample problems These problems are not the exact problems but by solving these you can understand the hardness of the original problems. Do the homework problems and the problems which I discussed in class . 1. Check whether or not the vector field is conservative F ( x, y, z ) = y 2 z 3 i + 2 xyz 3 j + 3 xy 2 z 2 k . 2. Use Green’s Theorem to evaluate the line integral along the given positively oriented curve C cos ydx + ( x 2 sin y ) dy C is the rectangle with the vertices (0 , 0) , (5 , 0) , (5 , 2) , (0 , 2). 3. Find the function f such that F = f and hence evaluate F . d r along the given curve C F ( x, y, z ) = e y i + xe y j + ( z + 1) e z k C : r (
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