Define f(x)={sin⁡(bx)x,x<0,ax2+b,0≤x<2,x+ab,x≥2.f(x)=\begin{cases} \dfrac{\sin(bx)}{x}, & x<0,\\ a x^{2}+b, & 0\le x<2,\\ \sqrt{x+ab}, & x\ge 2. \end{cases}…

Mathematics

Problem

Define f(x)={sin⁡(bx)x,x<0,ax2+b,0≤x<2,x+ab,x≥2.f(x)=\begin{cases} \dfrac{\sin(bx)}{x}, & x<0,\\ a x^{2}+b, & 0\le x<2,\\ \sqrt{x+ab}, & x\ge 2. \end{cases} Determine all real numbers aa and bb for which ff is continuous on the entire real line.

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