AP

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let g(x)=sin⁡xxg(x)=\dfrac{\sin x}{x} for x≠0x\neq0. (i) State the values of xx for which g(x)g(x) is defined. (ii) Explain, with reason, whether the derivative g′(x)g'(x) exists at x=0x=0. (iii) Hence determine the domain of g′(x)g'(x). Give your answer in interval notation.

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