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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. See more

# When Limits Don't Exist

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?

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

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

For which choice of $$a$$ is the above statement true?

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

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

Which limit(s) exist(s)?

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