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PrecalculusSuperchallengeIntroduction to Limits

Introduction to Limits · Superchallenge problem

Find constants aa and bb so that

f(x)={sin⁡(ax)x,x<0,b,x=0,x+4−2x,x>0,f(x)=\begin{cases} \dfrac{\sin(ax)}{x}, & x<0,\\[6pt] b, & x=0,\\[4pt] \dfrac{\sqrt{x+4}-2}{x}, & x>0,\end{cases}

is continuous at x=0x=0.