How do you estimate ∆f using the Linear Approximation and use a calculator to compute both the error and the percentage error given $f (x) = \sqrt{18 + x}$ $f(x)=sqrt(18+x)$ 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

$=0.05/5*100=1%$

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)f(x)=√18+xf(x)=sqrt(18+x) a=7, and ∆x=−0.5?