Which of the following limits represents

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

Problem

Which of the following limits represents f′(x)f'(x), the derivative of ff at the point xx? (a) lim⁡h→0f(x+h)−f(x)x\displaystyle\lim_{h\to 0}\dfrac{f(x+h)-f(x)}{x} (b) lim⁡h→0f(x+h)−f(x)h\displaystyle\lim_{h\to 0}\dfrac{f(x+h)-f(x)}{h} (c) lim⁡h→0f(x+h)−f(h)h\displaystyle\lim_{h\to 0}\dfrac{f(x+h)-f(h)}{h} (d) lim⁡h→0f(x+h)−f(x−h)h\displaystyle\lim_{h\to 0}\dfrac{f(x+h)-f(x-h)}{h}

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