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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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The graph of \(y = f(x)\) is pictured above. For which values of \(a\) in \(\{0, 1, 2\}\) does \[\lim_{x \to a} f(x)\] exist?

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Based on the graphs, which limit diverges to \(\infty\) as \(x \to 0?\)

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\[\lim_{x \to a} \frac{1}{x^2} = \text{ a (finite) number}\]

For which choice of \(a\) is the above statement true?

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Which option is true of \[A = \lim_{x \to \infty} \sin\left(x\right)?\]

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\[A = \lim_{x \to 0} \frac{x}{x}, \,\,\,\,\,B = \lim_{x \to 0} \frac{|x|}{x}\]

Which limit(s) exist(s)?

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