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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 Warmup

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

If the values of $$x$$ increase without bound, what do the values of $$x^2$$ approach?

$A = \lim_{x \to 3}x-9$

$B = \lim_{x \to 3}x^2-9$

$C = \lim_{x \to 3}x^3-9$

Which limit is equal to $$0?$$

$A = \lim_{x \to 0}\frac{1}{x}$

$B = \lim_{x \to 0}\frac{x}{x}$

$C = \lim_{x \to 0}\frac{x^2}{x}$

Which limit is equal to $$0?$$

$\lim_{x \to 0}\frac{x^3}{x^m} = 1$

What must be true of $$m$$?

$\lim_{x \to 5}\frac{x^2-10x+25}{\left(x-5\right)^2}$

If the value of $$x$$ approaches 5, what does the value of $$\frac{x^2-10x+25}{\left(x-5\right)^2}$$ approach?

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