Calculus
Limits of Functions
Find the value of
\[ \lim_{x \to -2} \frac{x^2+ 5x+6}{x+2}. \]
Evaluate
\[ \lim_{x \to 1} \frac{x-1}{\sqrt{x+3} -2}. \]
If \[\displaystyle \lim_{x \to a} \frac{x^3-a^3}{x^2-a^2}=9,\] what is the value of \[\lim_{x \to a} \frac{x^3-ax^2+a^2x-a^3}{x-a}?\]
If \( a\) and \(b\) satisfy
\[ \lim_{x \to 0} \frac{x}{\sqrt{x+a} - b} = 6, \]
what is \( a+b \)?
Evaluate
\[ \lim_{x \to \infty} \left( \sqrt{x^2 + 4x - 1} - x \right). \]