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8th - MATH 120 RECITATION QUESTIONS(WEEK 8 1 Find an...

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MATH 120 RECITATION QUESTIONS (WEEK 8) 1. Find an equation of the tangent plane to the given surface at the specified point. a ) z = p 4 - x 2 - 2 y 2 , (1 , - 1 , 1) b ) z = e x 2 - y 2 , (1 , - 1 , 1) 2. Explain why the function f ( x, y ) = x y is differentiable at the given point (6 , 3). Then find the linerization L ( x, y ) of the function at that point. 3. Find the linear approximation of the function f ( x, y ) = p 20 - x 2 - 7 y 2 at (2 , 1) and use it to approximate f (1 . 95 , 1 . 08) . 4. Find the differential of the function u = r s + 2 t . 5. if z = x 2 - xy + 3 y 2 and ( x, y ) changes from (3 , - 1) to (2 . 96 , - 0 . 95) , compare the values of Δ z and dz . 6. The pressure , volume , and temperature of a mole of an ideal gas are related by the equation PV = 8 . 31 T , where P is measured in kilopascals , V in liters, and T is kelvins.Use differentials to find the approximate change in the pressure if the volume increases from 12 L to 12 . 3 L and the temprature decreases from 310 K to 305 K . 7. a ) The function f ( x, y ) = xy x 2 + y 2 if ( x, y ) 6 = (0 , 0) 0 if ( x, y ) = (0 , 0) was graphed in Figure 4 in Stewart.Show that f x (0 , 0) and f y (0 ,
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