Finding the limit of limx →∞ ((x + 1) cosx)) / (x ^ 2 + 1)

The original limit = limx →∞ (1 / x + 1 / x ^ 2) * cosx / (1 + 1 / x ^ 2) is obtained by dividing the numerator and denominator by x ^ 2 at the same time. Obviously, at this time, both 1 / X and 1 / x ^ 2 tend to 0, while the denominator 1 + 1 / x ^ 2 tends to 1, and cosx is a bounded function. Therefore, the original limit = limx →∞ (1 / x + 1 / x ^ 2) * cosx / (1 + 1 / x ^ 2) = 0 / 1 = 0