Question [E] I (1) If w = 4y - 5y, find the percentage error in w at y = 1, if the error in y = 0.04. percent. (1) if Z = 4 cos w - 6w, find the relative percentage error in Z at w = 0, if the error in w = 0.005. percent (6) If Y = e + 3x2 + 4x, find the percentage error in Y at x = 2, if the error in x = 0.002. percent

Step1/3Part (i)We have \(w=4y^6-5y\)at \(y=1, \) the error in y \((Deltay)=0.04\)The percentage error in w \((Deltaw)=(dw)/(dy)|_(y=1)(Deltay)\)\((dw)/(dy)=d/dy(4y^6-5y)=24y^5-5\)at y = 1,\((dw)/(dy)=24(1)^5-5=19\)\(impliesDeltaw=19(0.04)=0.76\)at y = 1,\(w=4(1)^6-5(1)=-1\)The percentage error \(=(Deltaw)/w*100%\) \(=(0.76)/-1*100%=76%\)Explanation:calculation of percentage error.Step2/3Part (ii)We have \(Z=4cosw-6w\)at \(w=0,\) the error in w \((Deltaw)=0.005\)The percentage error in Z \((DeltaZ)=(dZ)/(dy)|_(w=1)(Deltaw)\)\((dZ)/(dw)=d/(dw)(4cosw-6w)=-4sinw-6\)at w = 0,\((dZ)/(dw)=-4sin0-6=-6\) {sin(0)=0}\(impliesDeltaZ=-6(0.005)=-0.03\)at w = 0,\(Z=4cos0-6(0)=4\) {cos(0)=1}The percentage error \(=(DeltaZ)/Z*100%\) \(=(-0.03)/4*100%\) \(=0.75%\)Step3/3Part (iii)\(Y=e^(x^2)+3x^2+4x\)at \(x=2,\) the error in x \((Deltax)=0.002\)The error in Y \((DeltaY)=(dY)/(dx)|_(x=2)(Deltax)\)\((dY)/(dx)=d/dx(e^(x^2)+3x^2+4x)=e^(x^2)(2x)+6x+4\)at x = 2,\((dY)/dx=(2*2)e^(2^2)+6(2)+4=234.3926\)\(impliesDeltaY=234.3926(0.002)=0.468752\)at x=1,\(Y=e^(2^2)+3(2^2)+4(2)=74.59815\)The percentage error \(=(DeltaY)/Y*100%\) \(=0.468752/74.598151*100%=0.628%\)Final Answer:Part (i)The percentage error = 76%Part (ii)The percentage error = 0.75%Part (iii)The percentage error = 0.628% ...