# Math Help - Continuity question.

1. ## Continuity question.

$g(x)=\left\{\begin{array}{cc}x^2+1,&\mbox{ if }x\leq 0\\x^2+bx\sin(\frac{1}{x})+c,&\mbox{ if }x>0\end{array}\right.$

Find all the values of b and c that make g continuous on R, express the values of b and c as sets.

$b\in$
$c\in$

2. The only possible point of discontinuity is at $x=0,$ hence, you must put $\lim_{x\to0^-}f(x)=\lim_{x\to0^+}f(x).$