Answer
True value: -0.02020;
Approximated value: -0.02
The difference in the two results: $-0.0002$
Work Step by Step
$f(x) =\ln x$
$f'(x)=\frac{1}{x}$
$dy=\frac{1}{x}dx$
Finding the value of this function at 0.98 means that our change in x is 0.02.
The differential expression thus approximates that the change in the function value is -0.02
$\ln1 +(-0.02)=-0.02$
The true value of this logarithm, found using a calculator, is $\ln 0.98=-0.02020$
The absolute value of the difference in the two results: $-0.0002$
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