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The valuc of $f(4)-f(3)$ is
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Verified Answer
The correct answer is:
$\Delta f(2)+\Delta^{2} f(1)+\Delta^{3} f(1)$
$f(4)-f(3)=\Delta f(3)$
$=\Delta[f(2)+\Delta f(2)]$
$[\because \Delta f(2)=f(3)-f(2)]$
$=\Delta f(2)+\Delta^{2} f(2)$
$=\Delta f(2)+\Delta^{2}[f(1)+\Delta f(1)]$
$=\Delta f(2)+\Delta^{2} f(1)+\Delta^{3} f(1)$
$=\Delta[f(2)+\Delta f(2)]$
$[\because \Delta f(2)=f(3)-f(2)]$
$=\Delta f(2)+\Delta^{2} f(2)$
$=\Delta f(2)+\Delta^{2}[f(1)+\Delta f(1)]$
$=\Delta f(2)+\Delta^{2} f(1)+\Delta^{3} f(1)$
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