Community Answer

Honor CodeSolved 1 Answer

See More Answers for FREE

Enhance your learning with StudyX

Receive support from our dedicated community users and experts

See up to 20 answers per week for free

Experience reliable customer service

Get Started

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% ...