Evaluate the following limits: a) _x infinity (x + sqrt(x2 - 4x + 1))

Here are the solutions to the limits problems.

Section A: Limits

1. Evaluate the following limits:

a) $\lim_{x \to \infty} (x + \sqrt{x^2 - 4x + 1})$

Step 1: Evaluate the terms as $x \to \infty$.
As $x \to \infty$, $x \to \infty$.
For the square root term, $\sqrt{x^2 - 4x + 1} \approx \sqrt{x^2} = x$ for large $x$.
So, the expression approaches $\infty + \infty$.

Step 2: Determine the limit.

$$$$