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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. See more

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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