Answer:
1/2
Explanation:
Find the following limit:
lim_(x->∞) (x + 1)/(1 x + sqrt(x)^2 + 1)
(x + 1)/(1 x + sqrt(x)^2 + 1) = (x + 1)/(2 x + 1):
lim_(x->∞) (x + 1)/(2 x + 1)
The leading term in the denominator of (x + 1)/(2 x + 1) is x. Divide the numerator and denominator by this:
lim_(x->∞) (1 + 1/x)/(2 + 1/x)
The expressions 1/x and 1/x both tend to zero as x approaches ∞:
Answer: 1/2