For a piecewise-defined function

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

Problem

For a piecewise-defined function, the derivative of ff at a point x=ax=a is most directly defined as which of the following limits, provided the limit exists? (a) lim⁡h→0+f(a+h)−f(a)h\displaystyle \lim_{h\to 0^+}\frac{f(a+h)-f(a)}{h} (b) lim⁡h→0f(a+h)−f(a)h\displaystyle \lim_{h\to 0}\frac{f(a+h)-f(a)}{h} (c) lim⁡h→0f(a+h)−f(a−h)2h\displaystyle \lim_{h\to 0}\frac{f(a+h)-f(a-h)}{2h} (d) lim⁡h→0f(a+h)−f(a)h2\displaystyle \lim_{h\to 0}\frac{f(a+h)-f(a)}{h^{2}}

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