How do you estimate ∆f using the Linear Approximation and use a calculator to compute both the error and the percentage error given #f(x)=sqrt(18+x)# a=7, and ∆x=−0.5?

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Answer 1 · 2017-07-30T19:11:47

The error is #Deltaf=-0.05# and the percentage error is #=1%#

The linear approximation is

#f(a+Deltax)=f(a)+f'(a)*Deltax#

Here,

#a=7#

#Deltax=-0.5#

#f(x)=sqrt(18+x)#, #=>#, #f'(x)=1/(2sqrt(18+x))#

Therefore,

#f(7-0.5)=f(7)-1/(2sqrt(18+5))*0.5#

#Deltaf=f(7-0.5)-f(7)=-1/10*0.5=-0.05#

The percentage error is

#=0.05/5*100=1%#