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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 \(\displaystyle \lim_{x \to 2^+} f(x)?\)

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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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