test1_sol

test1_sol - Mathematics 20E Spring 2009 Test 1 Name:...

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Unformatted text preview: Mathematics 20E Spring 2009 Test 1 Name: Section: ID: Be sure to show all work. Answers without full justification are worth no credit. Remember that you can often check your answers. You may use a single page of notes, but no other aids are allowed. This test consists of 4 questions. Each question is worth a total of 5 points. 1 /5 2 /5 3 /5 4 /5 /20 1) Let f : 3 2 be given by f ( x, y, z ) = parenleftbigg ( x 1) y + z xz 2 parenrightbigg and let g : 2 3 be such that g (1 , 2) = 1 1 and D g (1 , 2) = 1 1 1 2 1 . Find the linearization of ( f g ) at the point (1 , 2). First, notice that D f ( x, y, z ) = parenleftbigg y x 1 1 z 2 2 xz parenrightbigg . Now, the general form of the linearization of ( f g ) at (1 , 2) is given by l ( u, v ) = ( f g )(1 , 2) + D ( f g )(1 , 2) parenleftbiggparenleftbigg u v parenrightbigg parenleftbigg 1 2 parenrightbiggparenrightbigg ....
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test1_sol - Mathematics 20E Spring 2009 Test 1 Name:...

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