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Calculus › Continuity › Continuity of piecewise functions

Continuity with parameters a and b

High school · ●●○○○ 20 pts

Let f,g:R→Rf,g:\mathbb{R}\to\mathbb{R} be the functions f(x)={−x+3,x≤1,−ax2,otherwise,g(x)={x3+x2−x−1x−1,x≠1,−b,otherwise.f(x)=\begin{cases}-x+3,&x\leq 1,\\-ax^2,&\text{otherwise},\end{cases}\qquad g(x)=\begin{cases}\dfrac{x^3+x^2-x-1}{x-1},&x\neq 1,\\-b,&\text{otherwise}.\end{cases} Determine the parameters a,b∈Ra,b\in\mathbb{R} such that ff and gg are both continuous. Find aa and bb.

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one-sided limitslimits of rational functionspolynomial division