Search problems 2 problems match “one-sided limits”. Clear
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Continuity constant for a piecewise function ●○○○○ 10 ptsLet f ( x ) = { k x 2 if x ≤ 2 x + k if x > 2 f(x)=\begin{cases} kx^{2} & \text{if } x\le 2 \\ x+k & \text{if } x>2\end{cases} f ( x ) = { k x 2 x + k if x ≤ 2 if x > 2 k k k f f f Continuity with parameters a and b ●●○○○ 20 ptsLet f , g : R → R f,g:\mathbb{R}\to\mathbb{R} f , g : R → R f ( x ) = { − x + 3 , x ≤ 1 , − a x 2 , otherwise , g ( x ) = { x 3 + x 2 − x − 1 x − 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} f ( x ) = { − x + 3 , − a x 2 , x ≤ 1 , otherwise , g ( x ) = ⎩ ⎨ ⎧ x − 1 x 3 + x 2 − x − 1 , − b , x = 1 , otherwise . a , b ∈ R a,b\in\mathbb{R} a , b ∈ R f f f g g g a a a b b b