Tính các giới hạn sau: a) \(\mathop {\lim }\limits_{x \to + \infty } \frac\); b) \(\mathop {\lim }\limits_{x \to - \infty } \frac\); c) \(\mathop {\lim }\limits_{x \to + \infty } \frac{{\sqrt {{x^2} + 1} }}{x}\); d) \(\mathop {\lim }\limits_{x \to - \infty } \frac{{\sqrt {{x^2} + 1} }}{x}\); e) \(\mathop {\lim }\limits_{x \to 6} \frac{1}\); f) \(\mathop {\lim }\limits_{x \to {7^ + }} \frac{1}\).