Question 60
Prove that for every $x \in K \setminus L$ there exists $a, b \in L$ so that $x^{2013} + a x + b = 0$.
**8.** The function $f : \mathbb{R} \to [0, \infty)$ is continuous and $\lim_{x \to \infty} f(x) = \infty$. Prove that, for every $n \in \mathbb{N}^*$ and every $y \in \mathbb{R}$, there exists $t = t(n, y)$ so that $\int_y^t f(x) dx = n$.
**8.** The function $f : \mathbb{R} \to [0, \infty)$ is continuous and $\lim_{x \to \infty} f(x) = \infty$. Prove that, for every $n \in \mathbb{N}^*$ and every $y \in \mathbb{R}$, there exists $t = t(n, y)$ so that $\int_y^t f(x) dx = n$.