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SOLUTION 18: Begin with the function
f(x)=log(100x)
and choose
xvalues:0h4
so that
Δx=h40=h4

(Recall that D{log(g(x))}=1g(x)g(x)1ln(10).)

The derivative of  y=f(x)  is
f(x)=1100x(1)1ln(10) =1(1)(x100)1ln(10) =1x1001ln(10)
The exact change of yvalues is
Δy=f(h4)f(0) =log(100(h4))log(100+(0)) =log(100h4)log(100)

( Recall that log(10n)=n.)

=log(100h4)log(102) =log(100h4)2
The Differential is
dy=f(0) Δx =1((0)4)1001ln(10)(h4) =11001ln(10)(h4) =1100ln(10)h4
Since h is "small" we will assume that
Δydy     log(100h4)21100ln(10)h4     log(100h4)21100ln(10)h4

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