The function is defined by g(x)= cases ax x , & x<0

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

Problem

The function gg is defined by g(x)={sin⁡axx,x<0,bx2+1,x≥0.g(x)=\begin{cases} \displaystyle \dfrac{\sin ax}{x}, & x<0,\\ bx^{2}+1, & x\ge 0. \end{cases} For which value of aa does lim⁡x→0g(x)\displaystyle \lim_{x\to 0} g(x) exist and equal 11? (a) π2\dfrac{\pi}{2} (b) 11 (c) 00 (d) 22

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