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# Limits of Functions

What happens when a function's output isn't calculable directly – e.g., at infinity – but we still need to understand its behavior? That's where limits come in.

# Limits of Rational 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

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

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