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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.

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Evaluate

\[ \lim_{x \to \infty} (2x-3). \]

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Evaluate \[ \lim_{x \to \infty} \frac{3}{x^2}. \]

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Evaluate \[ \lim_{y \to \infty} \frac{y+2}{y-3}. \]

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Evaluate

\[ \lim_{x \to \infty} \frac{2^x}{x^2}. \]

Hint: You can refer to the following graphs of \( y= 2^x \) and \( y= x^2 \).

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Evaluate

\[ \lim_{ t \to \infty} \left( \frac{1}{t-2} + 1 \right). \]

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