Answer to Question #283829 in Quantitative Methods for Miko

Question

Let be a real number. Let x~2.5 be an approximate value of with absolute error

at most 0.01. The function ( )

is evaluated at instead of . Estimate the absolute error

Answer 1

for example $f(x)=x^2$

then absolute error of f(x) at x = 2.5:

$|f(x+\Delta x)-f(x)|=f(2.51)-f(2.5)=2.51^2-2.5^2=0.0501$