y = x+1 este asimptotă oblică spre + ꝏ dacă:
[tex]\lim\limits_{x\to \infty} f(x) - \lim\limits_{x\to \infty} (x+1) = 0 \\ \\ \lim\limits_{x\to \infty}\Big[ f(x) - (x+1) \Big] = 0 \\ \\ \lim\limits_{x\to \infty}\Big[ \dfrac{x^2+px+1}{x+1} - (x+1) \Big] = 0 \\ \\\lim\limits_{x\to \infty}\dfrac{x^2+px+1 - (x+1)^2}{x+1}= 0 \\ \\ \lim\limits_{x\to \infty}\dfrac{x^2+px+1 - x^2 - 2x - 1}{x+1}= 0 \\ \\ \lim\limits_{x\to \infty}\dfrac{(p-2)x}{x+1}= 0 \\ \\ (p-2)\cdot \lim\limits_{x\to \infty}\dfrac{x}{x+1}= 0 \\ \\ (p-2)\cdot 1 = 0 \Rightarrow\boxed{p= 2}[/tex]
