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akers2 - Math 22 Exam 2C Akers FS 00 1(10 pts Given 2(5 pts...

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Math 22 Exam 2C Akers — FS 00 1) (10 pts) Given ( , ) co s2 y fx y x y ey = +- find ,,, xy x x yy ffff and xy f . 2.(5 pts) Given 3 co s4 z z yx - =+ , find z x . 3.(10 pts) Use the Chain Rule to find w s when s=1 and t=0 if 2 w xyz + 2 22 , 1 , ( 1) t x es y t z st = + = + =- . 4.(10 pts) Find the equations of the tangent plane and the normal line to the surface 2 z z +-= at the point (1,2 , 2) - . 5a. (10 pts) Find the rate of change of 2 (, )2 z fx y = =- at the point (1,5) in the direction of 3,4 - . 5b. (5 pts) In 5a. above, at the point (1,5), what is the direction of the maximum rate of change of the function and what is the magnitude of this maximum rate of change? 6. (10 pts) Show the following limit does not exist and clearly show why. ( 29 ( 29 2 42 , 0,0 2 lim + 7. (10 pts) Given (,) y yx == , find the linearization (,) Lxy for fxy at the point (4,1) and use it to approximate the value of (1.1 ) 3.92 . Compare your approximation with your calculator’s value. =__________________ 8. (15 pts) Given 2 11 ( , )7 y x y = + ++ , find and classify all critical points of
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