Evaluate the following limits: a) lim x->inf (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: Factor out $x^2$ from the square root term.

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