Let f(x)= cases (ax) x , & x 0, 2, & x=0

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let f(x)={sin⁡(ax)x,x≠0,2,x=0.f(x)=\begin{cases} \dfrac{\sin(ax)}{x}, & x\neq0,\\ 2, & x=0. \end{cases} Determine the value of aa that makes ff continuous at x=0x=0. (a) 11 (b) 22 (c) 00 (d) π2\dfrac{\pi}{2}

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