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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 - To Infinity

Evaluate

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

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

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

Evaluate

$\lim_{x \to \infty} \frac{2^x}{x^2}.$

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

Evaluate

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

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