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Calculus
# Limits of Functions

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Find the value of

\[ \lim_{x \to -2} \frac{x^2+ 5x+6}{x+2}. \]

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Evaluate

\[ \lim_{x \to 1} \frac{x-1}{\sqrt{x+3} -2}. \]

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If \( a\) and \(b\) satisfy

\[ \lim_{x \to 0} \frac{x}{\sqrt{x+a} - b} = 6, \]

what is \( a+b \)?

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Evaluate

\[ \lim_{x \to \infty} \left( \sqrt{x^2 + 4x - 1} - x \right). \]

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