Home › JEE Advanced › Calculus › If $y=f(x)$ and $\Delta x$ is small, the differe…
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.
Related questions
A tank is draining and a student is asked how fast the depth falls when the volume is chanThe notation used for a family of antiderivatives, complete with its constant, is the:Knowing an object's velocity, a student recovers its position by finding an:A function whose derivative is the given function is called its:Calculators and computers rely on that same tangent-based idea when they find:An iterative technique for finding zeroes, built on tangent line approximations, is:The rule that resolves such a limit by differentiating numerator and denominator separatelA limit produces the form zero over zero, so its behaviour cannot be read off directly. Th