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1. Limit of binomial coefficient over quadratic ●○○○○ 10 ptsCalculate $\lim_{n \to \infty} \frac{\binom{n}{2}}{n^2+1}$. Give your answer as a decimal.
2. Continuity with parameters a and b ●●○○○ 20 ptsLet $f,g:\mathbb{R}\to\mathbb{R}$ be the functions $$f(x)=\begin{cases}-x+3,&x\leq 1,\\-ax^2,&\text{otherwise},\end{cases}\qquad g(x)=\begin{cases}\dfrac{x^3+x^2-x-1}{x-1},&x\neq 1,\\-b,&\text{otherwise}.\end{cases}$$ Determine the parameters $a,b\in\mathbb{R}$ such that $f$ and $g$ are both continuous. Find $a$ and $b$.