Question

f(x)= x-1/x
ecuatia asimptotei oblice spre +infinit

Answer 1

$\lim\limits_{x\to \infty}\Big(x-\dfrac{1}{x}-mx-n\Big) = \\ \\ =\lim\limits_{x\to \infty}\dfrac{x^2-1-mx^2-nx}{x}= \\ \\ =\lim\limits_{x\to \infty}\dfrac{(1-m)x^2-nx-1}{x} = 0 \\ \\ \Rightarrow 1-m = 0\quad si\quad n = 0 \Rightarrow m = 1\quad si\quad n = 0 \\ \\ y = mx+n\\ \\\Rightarrow y = x,\quad \text{asimptota oblica spre }+ \infty$