Calculus
# Limits of Functions

If $\lim_{x \to 4} \frac{f(x) - 5}{x-2}=1,$ find $\displaystyle \lim_{x \to 4} f(x).$

Find the value of

$\lim_{x \to \infty} \left( \sqrt{x^2 + \lfloor x \rfloor} - x \right).$

**Assumptions and Details:**

$\lfloor \cdot \rfloor$ is the floor function such that $\lfloor x \rfloor = n$ if $n \leq x < n+1,$ where $n$ is an integer.