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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

# One-Sided Limits

If $$f(x)$$ is the function $f(x)= \begin{cases} -x+10 & \text{ if } \lvert{x}\rvert \leq 2, \\ 2x^2 & \text{ if } \lvert{x}\rvert > 2, \end{cases}$ what is $$\displaystyle \lim_{x \to 2^+} f(x)?$$



What is the value of

$\lim_{x \to 3^-} \frac{x^2 - 1}{x-2}?$

Find the limit of

$\lim_{x \to -1^+} \frac{x^2+x}{ |x+1| }.$

What is the value of $\lim_{x \to 0^+} \frac{\lvert{4x}\rvert}{x}-\lim_{x \to 0^-} \frac{\lvert{4x}\rvert}{x}?$

What is the value of

$\lim_{x \to 3^+} \sqrt{x-3} ?$

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