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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 \[\lim_{x\to 5} 1.\]

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True or False?

\[\lim_{x\to 0} \frac{1}{x} = \infty.\]

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Suppose \[\lim_{x\to \infty} f(x) = \infty \text{ and } \lim_{x\to \infty} g(x) = \infty,\]

and

\[L = \lim_{x\to \infty} (f(x) - g(x)).\]

Is it possible that \(L = 0\)?

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Suppose \[\lim_{x\to \infty} f(x) = \infty \text{ and } \lim_{x\to \infty} g(x) = \infty,\]

and

\[L = \lim_{x\to \infty} (f(x) - g(x)).\]

Is it possible that \(L = -\infty\)?

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