Identify the correct mathematical definition of instantaneous velocity for a particle…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Identify the correct mathematical definition of instantaneous velocity vv for a particle whose displacement is x(t)x(t): (a) v=ΔxΔtv=\dfrac{\Delta x}{\Delta t} (b) v=lim⁡Δt→0ΔxΔtv=\displaystyle \lim_{\Delta t \to 0} \dfrac{\Delta x}{\Delta t} (c) v=x(t)tv=\dfrac{x(t)}{t} (d) v=lim⁡Δt→0∣Δx∣Δtv=\displaystyle \lim_{\Delta t \to 0} \dfrac{|\Delta x|}{\Delta t}

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