Which of the following limit expressions is equal to for a differentiable function at ?

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

Problem

Which of the following limit expressions is equal to f′(a)f'(a) for a differentiable function ff at x=ax=a? (a) lim⁡h→0f(a+h)−f(a)a\displaystyle \lim_{h\to 0}\frac{f(a+h)-f(a)}{a} (b) lim⁡x→af(x)−f(a)x\displaystyle \lim_{x\to a}\frac{f(x)-f(a)}{x} (c) lim⁡Δx→0f(a+Δx)−f(a)Δx\displaystyle \lim_{\Delta x\to 0}\frac{f(a+\Delta x)-f(a)}{\Delta x} (d) lim⁡x→af(a)−f(x)x−a\displaystyle \lim_{x\to a}\frac{f(a)-f(x)}{x-a}

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