Identify the correct limit expression that represents at a general point .

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

Problem

Identify the correct limit expression that represents ddx(x3)\dfrac{d}{dx}\bigl(x^{3}\bigr) at a general point xx. (a) lim⁡h→0(x+h)3−(x−h)3h\displaystyle \lim_{h\to0}\frac{(x+h)^{3}-(x-h)^{3}}{h} (b) lim⁡h→0(x−h)3−x3h\displaystyle \lim_{h\to0}\frac{(x-h)^{3}-x^{3}}{h} (c) lim⁡h→0(x+h)3−x3h\displaystyle \lim_{h\to0}\frac{(x+h)^{3}-x^{3}}{h} (d) lim⁡h→0(x+h)3−x3h2\displaystyle \lim_{h\to0}\frac{(x+h)^{3}-x^{3}}{h^{2}}

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