Question

The values of constants \( a \) and \( b \), so that \[ \lim_{x \to \infty} \left( \frac{x^2 + 1}{x + 1} - ax - b \right) = 0 \] are:

• A. \( a = 0, b = 0 \)
• B. \( a = 1, b = -1 \)
• C. \( a = -1, b = 1 \)
• D. \( a = 2, b = -1 \)

Hint:

When solving limits, simplify the expression and balance terms to satisfy the condition for the limit.

Answer 1

The Correct Option is B

Step 1: Analyze the expression.
Simplify the given expression and use limits to find the values of \( a \) and \( b \).
Step 2: Conclusion.
Thus, \( a = 1 \) and \( b = -1 \).
Final Answer: \[ \boxed{1, -1} \]