Bruk lineær approksimasjon til å estimere 4,1\sqrt{4{,}1}4,1.
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La f(x)=xf(x) = \sqrt{x}f(x)=x, a=4a = 4a=4. f(4)=2f(4) = 2f(4)=2, f′(x)=12x\displaystyle f'(x) = \frac{1}{2\sqrt{x}}f′(x)=2x1, f′(4)=14\displaystyle f'(4) = \frac{1}{4}f′(4)=41. f(4,1)≈2+14(0,1)=2,025\displaystyle f(4{,}1) \approx 2 + \frac{1}{4}(0{,}1) = 2{,}025f(4,1)≈2+41(0,1)=2,025. (Eksakt: 2,02485...2{,}02485...2,02485...)
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