If $y=f(x)$ and $\Delta x$ is small, the differential approximation for the corresponding small change in $y$ is
A$\Delta y=\dfrac{\Delta x}{dy/dx}$
B$\Delta y=\left(\dfrac{dy}{dx}\right)\Delta x$
C$\Delta y=\dfrac{d^2y}{dx^2}\Delta x$
D$\Delta y=y\Delta x$
Answer & Solution
Correct answer: B. $\Delta y=\left(\dfrac{dy}{dx}\right)\Delta x$
In error approximation, for a small change $\Delta x$, the corresponding approximate change in $y$ is $\Delta y\approx dy=\left(\dfrac{dy}{dx}\right)\Delta x$. This is the linear approximation formula.
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