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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 \(f(x)\) is a function defined on the real numbers and \[\lim_{x\to a} f(x) = L.\] Which of the following must be true?
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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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