Chapter 15 - Section 15.1 - Functions of Several Variables from the Numerical, Algebraic, and Graphical Viewpoints - Exercises - Page 1094: 3

$$\eqalign{ & \left( a \right)0 \cr & \left( b \right)0.2 \cr & \left( c \right) - 0.1 \cr & \left( d \right)0.2a + 0.2 - 0.02a \cr & \left( e \right)0.2y + 0.1x - 0.01xy \cr & \left( f \right)0.2\left( {x + h} \right) + 0.1\left( {y + k} \right) - 0.01\left( {x + h} \right)\left( {y + k} \right) \cr} $$

$$\eqalign{ & f\left( {x,y} \right) = 0.2x + 0.1y - 0.01xy \cr & \left( a \right){\text{ Find }}f\left( {0,0} \right) \cr & f\left( {0,0} \right) = 0.2\left( 0 \right) + 0.1\left( 0 \right) - 0.01\left( 0 \right)\left( 0 \right) \cr & f\left( {0,0} \right) = 0 \cr & \cr & \left( b \right){\text{ Find }}f\left( {1,0} \right) \cr & f\left( {1,0} \right) = 0.2\left( 1 \right) + 0.1\left( 0 \right) - 0.01\left( 1 \right)\left( 0 \right) \cr & f\left( {1,0} \right) = 0.2 \cr & \cr & \left( c \right){\text{ Find }}f\left( {0, - 1} \right) \cr & f\left( {0, - 1} \right) = 0.2\left( 0 \right) + 0.1\left( { - 1} \right) - 0.01\left( 0 \right)\left( { - 1} \right) \cr & f\left( {0, - 1} \right) = - 0.1 \cr & \cr & \left( d \right){\text{ Find }}f\left( {a,2} \right) \cr & f\left( {a,2} \right) = 0.2\left( a \right) + 0.1\left( 2 \right) - 0.01\left( a \right)\left( 2 \right) \cr & f\left( {a,2} \right) = 0.2a + 0.2 - 0.02a \cr & \cr & \left( e \right){\text{ Find }}f\left( {y,x} \right) \cr & f\left( {y,x} \right) = 0.2y + 0.1x - 0.01xy \cr & \cr & \left( f \right){\text{ Find }}f\left( {x + h,y + k} \right) \cr & f\left( {x + h,y + k} \right) = 0.2\left( {x + h} \right) + 0.1\left( {y + k} \right) - 0.01\left( {x + h} \right)\left( {y + k} \right) \cr} $$