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Question 1 Use the total differential to quantify the following value. Not yet answered (1.97)2(8.97)−22(9) Marked out of 7.50 Flag question Step 1 We need a function z=f(x,y) such that the quantity can be represented by f(x+Δx,y+Δy)−f(x,y) for some x and Δx Let z=f(x,y)=xy Step 2 If (1.97)2(8.97)−22(9)=f(x+Δx,y+Δy)−f(x,y) then x=y=​ and dx=Δx= and dy=Δy=​
The total differential dz for the function z=f(x,y) is dz=ydx+2dy. Step 4 Substitute the values of x,y,dx, and dy in the equation and simplify. Therefore, (1.97)2(8.97)−22(9)=Δz≈dz=